Currently, there is no medical drug for stopping organ rejection. On the WIKI it says that there is a 2% chance of organ rejection curing itself with inaprovaline, but there was a conversation in the department hub discord of this not actually working. In 2015 there was a suggestion to add something like this called Amonozine. It was suggested to have acted as a:
"Light immunosuppressant -- A drug which, when administered, starts messing with the receiving organism and the transplanted organ. It outright combats rejection, and also, eventually, makes the organ fully fitting for the receiving organism. The only limitation is that the drug only works when the donor species is the same as the receiving species. If the species do not match, this will have no effect whatsoever. Otherwise, should have no real side-effects."
In the code under:
code/modules/organs/organ.dm
line 243, 244, and 245 say:
/obj/item/organ/proc/handle_rejection()
// Process unsuitable transplants. TODO: consider some kind of
// immunosuppressant that changes transplant data to make it match.
Showing that it was meant to be considered but since it was suggested back in 2015, I think it never actually made it to the code and was forgotten about.
I think medical should have an immunosuppressant to combat organ rejection with same-species organs. Characters who are fully against robot organs in their person have no other option but the monkey organ. Since all monkeys are A+ blood type, I don't think this drug should be unusable on donor organs given to different blood types than the donor body.
Here is the 2015 suggestion.