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The last different "species" that homo sapiens could crossbreed with was Neanderthals and it looks like it came at a great cost, there are good reasons to believe it produced infertile males or that males received some other fatal genetic flaw that removed them from the genetic pool, thus affecting the distribution of genes along the X and Y chromosomes. If these difficulties occurred despite Neanderthals being that much closer to us, then there's little chance that monkey sex will produce anything viable.
