it’s worth noting that the koboldification/dragonization process the exact same ritual by which a dragon becomes gravid with a child. (any gross biological mating process is but an unnecessary formality.)
and the ‘hrt’ question is literally the dragon’s own flame. their breath can destroy most things, but if an object is first graven by their claw, then it is also, on a deeper level, ‘carved’ into a vessel for their flame, granting them power over what the flames burn and how.
they can breathe the fire of life into things. treasures can be enchanted, while enflamed living creatures may slowly turn into kobolds (and/or simply lay a clutch of kobold eggs)
thus, it is within the power of a willing dragon to, for instance, let their flames persist as nothing more than a scar on your flesh and a warmth felt in every heartbeat
(dragon blood also works, esp. for wyrms without breath. metaphysically, dragon blood is equivalent to flame; it’s just rarely practiced. archaic, unhygienic, even blasphemous)
anyway, assuming you formed deep enough relationships with every single one of those dragons, and they were interested in indulging this experiment…
…the boring answer is that you might just turn to ash from having that much dragon flame in you
…the slightly less boring answer is that you might just turn into a dragon and later (or immediately) become gravid with a clutch of your lovers’ young. dragon reproduction is voluntary, and it is entirely natural for an egg to come years, decades after the sire’s flame was kindled.
…but the most interesting case is if the flame of each additional dragonsire blooms into its own heart of hearts (the source of blood and flame), yet all sharing the same body — yours.
in other words: you’d become a hydra, though of course whether this is still “you” depends on how you feel about that pronoun becoming distinctly more plural.
interestingly, if these are separate hearts, then there’s an angle for explaining a hydra’s proclivity for growing new heads. the body of a budding hydra soon becomes a compromise between the multiple competing hearts (dragons are innately quarrelsome), growing specifically to keep each the heart and flame separate
the popular impression of what happens when you cut off a hydra’s head, then, is no more than a consequence of it spilling so much blood — blood being exactly what prompts the birth of new dragons. (even moreso if the hydra, say, closes the wound with cauterizing fire.)
for a hydra, this doesn’t result in self-fertilization, perhaps because the proximity and intimacy of the heads far outstrips what even two mates might share. (and of course, because dragon reproduction is voluntary)
…which does raise the question of whether two truly deeply devoted lovers might gain new heads in the image of each other. but i’m getting off track, aren’t i?
hopefully that answers your question!