If humans die out tomorrow the two most likely candidates to achieve sapience after us are our closest genetic relatives. One of these, chimpanzee, has been discussed quite thoroughly in stories such as 'Planet of the Apes', but chimps have been done and are boring. We have another relative, just as closely related to us but rarely remembered, the Bonobo. These poor apes are fascinating with many uniquely 'human' traits not shared by any other species and some other rather unique aspects such as being arguably more peaceful and empathetic then humans and being a society run by the ladies. I feel one could make a really interesting species and culture by extrapolating what happens if bonobos reached sapience and these poor apes really deserve more love.
Of course speaking of love one can't really discuss the bonobo without discussing their unique conflict resolution strategy, commonly cited as a 'make love not war' policy. Put simply they have sex, lots of sex! It's used far beyond reproduction, as a means to mediate conflict, to build stronger social bonds, as something to trade for food or other resource, I could go on. They do it in every possible combination of sexes and positions you can think of as well, about the only thing off limits is reproductively mature adults mating with opposite sex relatives due to the risk of inbreeding. One could hardly write about sapient bonobo's without at least touching on their conflict resolution method.
Of course such a strategy is prone to spread of sexually transmitted infections (STI)s. Right now Bonobo survive mostly by having small enough numbers to make the odds of an STI evolving a bit lower and being isolated in troops enough that even if an STI shows up and ravages one troops it may not successfully spread to others.
As humans have discovered though as civilization grows so to does the risk of threatening diseases, at least until you have a good understanding of sanitation and how diseases spread. If bonobos started to move past troops to larger social organizations, and further more as trade and interaction between such groups grew, the odds of spread of STIs would likewise grow. It would be reasonable to believe Bonobo's would evolve (either physically or culturally) away from such heavy sexual activity to mitigate the risk of STI spread once this became an increasingly likely outcome of growing civilization.
Now I wouldn't be that upset if the amount of sexual contact was lowered in an evolved sapient bonobo population, in fact It would make it a bit easier to write them without the obvious complications of trying to write about such a sexually active species. However, many of the more fascinating aspects of bonobos, their heavy empathy, the female dominated social structures, how they interact with each other etc., all derives from their conflict resolution strategy. If it goes away then lots of the other interesting aspects will fade away as well and you just end up with a species that is effectively human.
So how could the bonobo evolve in such a manner that they keep at least some of their conflict resolution strategy, enough that we don't lose all the aspects of their psychology and culture that makes them unique, even as the risk of STIs grows within their civilization?