Some of these ideas are one step from being written, and some of them are completely vague. So I wouldn't bother with reviews of "why this is so small?" category. Any idea is good for adoption (like a half-challenge), because I don't have a time to write them all (don't know if I would be able to write even one of them, to tell you the truth). But if you want to do it, please say about that, so I would be able to read the result.

UPDATE: Had chosen to add all of my HSDxD crossover ideas here.

1)Unnamed High School DxD / Dragons Rioting crossover

Summary of idea:

Rintaro health problems stems from Sacred Gear malfunction. One of the girls at Nangokuren(most likely "Black Crow" Erin) happens to be Devil (Mid-Class one, either Queen, or Bishop in case of Erin) and Rintaro uses summoning contract with a wish to receive help with it. At the result he is resurrected as a Devil (either as a payment, or because it was needed to remove problem). Rintaro-centric. No mention of Rias' Peerage (at least early), because most of the HSDD canon happened several years before.

More in-depth description:

Rintaro recieves (mysteriously, of course) summoning circle right after first day (probably right after first encounter with 2 of the Dragons) and his knowledgeble-but-perverted-sidekick roommates (am I only one, who thinks of them as of deformed Motohama and Matsuda from HSDD?) explain to him rumor of that circle being real miracle-worker, which had not really any info about that, but the fact that they are real and helps with ANY request (there is the fact, that everyone used summoning circle was sworn to secrecy, and most of unreasonable wish-givers had been memory-modified, that works for that rumor mill still being just rumors and not a complete exposion of supernatural world).

After the first night in dormitory and happenings of the next morning, where his self-proclaimed student managed to find a way inside, Rintaro became desperate and tried that contract. Firstly, when Erin walks out after summoning, Rintaro starts panicking. But later girl manages to pry his problem from him and performs as usual (with using that weird app for cost of his wish). There she founds that the cost of his wish is joining of the same Peerage as she is in, summons her King (this one can be any character, maybe even OC). Both devils perform some research for the reason of "illness" and for the ways of its removal, where they found out that Rintaro is hanyou (preferably on the side of his mother, because she is an unknown character for now) that has SG inside of him, but his supernatural half clashes badly with his Sacred Gear. And the reason of his illness is that both parts were trying to activate at the similar time and it just happened to be that he was sexually excited first time it happened, thus the phenomen tied itself to that state of his body/mind.

They find out that Rintaro needs 3rd type of energy to work as mediator but he is not mature enough for his human energy work that way, thus his Reincarnation to the Devils helping him (where Devil energy will work as mediator).

After Reincarnation, the canon part of Dragons Rioting comes the same with the only difference that Rintaro does his funny stunts not out of necessity, but out of habit, and stops himself right afterwards.

P.S. The whole "hanyou having problems with his SG" part is not so far-fetched, after all there is at least one character from HSDD canon, who goes under that criteria (even if Gasper had troubles with control of his power and SG, but not with health)

Possible SG/youkai heritage conflict is:

Fire/Water(Ice)

Mermaid/Undine/Mizuchi/Yukionna (well any water/ice elemental or demi-elemental-like supernatural species) heritage with fire SG. Possible SGs (taken from wiki as either non-fictional but mythological/folklore things or fictional but unique things(so there are no simple flame-imbued weapons from games) from wherever):

1)Agneyastra, the god of fire Agni possess a weapon that would discharge and emit flames inextinguishable through normal means.

Not the best possibility, 'cause it's a weapon of god, so it shouldn't be SG by HSDD rules.

2)Lúin of Celtchar (also Spear of Fire or Spear of Destiny), a spear forged by the Smith of Falias for Lugh to use in his fight against Balor.

I don't really like this one, because of it's legends: "whenever the blood of enemies is about to flow from the lance, a cauldron full of venom is required to quench it; otherwise, the lance will blaze up in the fist of the man carrying it, and it will pierce him or the lord of the royal house. Each thrust of this lance will kill a man, even if it does not reach him; if the lance is cast, it will kill nine men" and "Obviously, the weapon needed to be handled with extreme care. According to his death-tale, Celtchar was accidentally killed by his own spear in a way which emphasises its excessive heat. When he had used the Lúin to slay a hound which had been ravaging the country, he placed it upright with the spear-point upwards and so a drop of the hound's blood which trickled down along the spear went through him and killed him". Both pieces taken from wiki depicts really tricky if not bloodthirsty (to the point of slaying of its own weilder) weapon.

3)Kongō, A trident-shaped staff which emits a bright light in the darkness, and grants wisdom and insight. The staff belonged originally to the Japanese mountain god Kōya-no-Myōjin. It is the equivalent of the Sanskrit Vajra, the indestructible lightning-diamond pounder of the king of the gods/rain-god Indra. There the staff represents the three flames of the sacrificial fire, part of the image of the vajra wheel.

Same as the first with added problem of being not mainly Fire-artifact. Heck, Kongous' main attribute is its indestructability.

4)Firebird's plumage, the feathers of a Firebird that glows brightly emitting red, orange, and yellow light, like a bonfire that is just past the turbulent flame. The feathers do not cease glowing if removed, and one feather can light a large room if not concealed. (Slavic mythology)

Also not the best one, cause this one mythic bird is more Warm+Light than Fire-oriented. And there are no any legends depicting it causing fire erupting. Heck one of them even goes with hero stealing that bird and bringing it around tightly bound by simple cloth!

5)Areadbhar (also Areadbhair), belonged to Pisear, king of Persia. Its tip had to be kept immersed in a pot of water to keep it from igniting, a property similar to the Lúin of Celtchar.

6)Amol Saiqa (from Magi) is the Metal Vessel of Alibaba Saluja. It gets its power from Alibaba's Djinn, Amon. It has the ability to generate Heat Magic and absorbs fire. It also has immense cutting power, as it can cut just about anything. Have another form (which can be used as Balance Breaker) in Amon no Hōken, where his attack range is slightly larger than the sword, so if his sword doesn't hit the opponent the heat produced around the sword is able to slice and enhance the range of the attack. Plus couple of Fire-based techs. Amon himself is a fire Djinn and the Djinn of Politeness and Austerity.

7)Fire-based Zanpakuto from Bleach (Ryujin Jakka, Tengumaru, Raika or Tobiume)

Some kind of fire creature (for now i have only Houou aka phoenix, salamander, fire-nymphs a.k.a. lampads and Efreeti as possibilities, but mostly they aren't good enough for this case) with water/ice SG

1)Varunastra, the god of water Varuna possess a weapon that would discharged and release torrential volumes of water. This weapon is commonly mentioned as being used to counter the Agneyastra. Also known for its shapeshifting properties.

Pretty much same complains as with its fire counterpart.

2)Mímisbrunnr, a well associated with the being Mímir, located beneath the world tree Yggdrasil. The water of the well contains much wisdom, and that Odin's eye sacrifice to the well was in exchange for a drink from it. (Norse mythology)

Not the well itself, but some kind of cup changed by its water? Not a possibility before really big change and adjustion.

3)Icingdeath from R. E. Salvatore Dark Elf books series. Scimitar with an Ice enchantment. Also is a frostbrand (as in specifically anti-fire) weapon. The weapon absorbed fire and heat, protecting its wielder against fire. It also had the ability to extinguish magical fire.

One of the best possibilities (if not for the fact, that i don't have good fire creature heritage in mind)

4)Valefor's Metal Vessel (from Magi) is a golden necklace with a red jewel at its center. Valefor is a water Djinn which specializes in Ice Magic and the Djinn of Falsehood and Prestige.

5)Vinea's Metal Vessel (again from Magi) is a golden hair pin. Vinea is a water Djinn and the Djinn of Sorrow and Isolation. Vinea has the ability to control the 2nd type of Magic, Water

6)Sharrar Rasas (and Magi strikes one more time!) is a magic tool used by Umm Madaura's Crew. It uses Water Magic that releases a blast of water shaped like a bullet, which is capable of blasting people several feet away. It can be hidden to look as if it is a sword.

7)Water/Ice-bazed Zanpakuto from Bleach (Hyourinmaru, Sode no Shirayuki or Nejibana. Maybe even Tiburon, oh that idea!)

2)"Let's show them real dragon, Ddraig!" High School DxD / Dragons Rioting crossover

Summary of idea:

Issei transfers to Nangokuren after Rias' graduating from school. He isn't yet ready to create his own Peerage (haven't received EP set yet, because of some formalities), but already seeks members. And what better members there can be, than beautiful, yet strong babes of famous Nangokuren?! Then he sees weird guy, who not simply shies from girls (that is normal and understandable, if rare), but actively runs from them! What the hell is wrong with that guy?!

Later Issei founds Rintaros' problem and chooses to help him and mentor him in Perverts' Way. Issei-centric.

Rintaros' illness can be either really illness (then Issey asks Asia to heal poor sod), or have the same reason as in the first idea. The healing wouldn't happen before festival.

A/N Yes, I know that this is similar to AI the Originals' story "Let's go, Rito". It actually was a fic, which branched this idea from previous one.

3)"Devils in the kitchen" Highschool DxD/Shokugeki no Soma crossover

Summary of idea:

What if Nakiri is a devil family? They aren't combat-oriented, like others, but prefer to be best at cooking (their family sin is either Gluttony or strange version of Pride where they are proud not of themselves, but of their cooking). They give the best of Tootsuki alumnis a choice to join their Peerages.

Erina is a half-devil (but she doesn't know because of that nasty thing with her father) and her Gods' Tongue is a Sacred Gear. Hayama is a pure human with SG as well. Out of the known characters (by the point of introduction of Azami), there are only Doujima and Alices' mother Eleonora, who were turned into devils. Doujima is a Rook for director himself, while Eleonora is a Bishop of her husband.

4)Negima/HSDxD crossover

So, had seen couple of stories with OP MCs being dropped in the world of Devils , usually into Peerage of Satans (so far had seen Ichigo as Pawn for Lucifer, Naruto as Queen for Belzebub and Shirou as Queen for Leviathan) and here i ignore all reincarnation and AU fics, otherwise number of those fics would have been bigger. Then had chosen to check out one of my favorite fandoms, and was horrified to find almost nothing with it (well, there ARE some fics with this crossover, but all of them either frozen or completely abandoned. plus out of them all, the only promising was with Chisame as MC). So here i go.

Summary of idea:

At the end of their fight, Lifemaker had banished Negi out of the Magicus Mundus. Normally, that woukd mean that either Negi would have dropped out of portal onto the Earth, or would have been left into the space on the Mars (which considering Negi's power and state at that point of time, wouldn't have been deadly for him). But with magical dimension being unstable, Negi had found himself on the other Earth (uncnowingly, at that) so he had been left stranded on familiar, yet different world.

A/N There, probably, should be a couple of chapters about Negi trying to find anything he knows (like Mahora Academy), then understanding that it is a different world (he IS a genius, so he should understand it, even if he would be in denial for some time, what with there being possibility of illusionary world). After that there should be some kind of encounter with devils, in result of which he will become a Queen (Negi is a mage, who is extremely fast and capable in close combat. Plus he is durable albeit in unusual way, so using something else is stupid) of one of Satans? preferably Leviathan (the reason is threefold: 1-out of the 3 Satans with unknown Queens, she is the most proactive one; 2-she is a girl, and Negi is Negi ^_^; 3-Falbium most likely wouldn't choose him, and Ajuka+Negi combo is too science-oriented for my tastes). Storyline would start long before HSDxD canon. Probably 10-12 years earlier, that way we can see a mature Negi by the canon time. He can also become a teacher at Kuoh.

A.N.: Had chosen to add some more possibilities for Sacred Gears in first idea here by going to couple of other sources.