Homoploid hybrid speciation (HHS) involves the recombination of two differentiated genomes into a novel, functional one without a change in chromosome number. Theoretically, there are numerous ways for two parental genomes to recombine. Hence, chance may play a large role in the formation of a hybrid species. If these genome combinations can evolve rapidly following hybridization and sympatric situations are numerous, recurrent homoploid hybrid speciation is a possibility. We argue that three different, but not mutually exclusive, types of contingencies could influence this process. First, many of these “hopeful monsters” of recombinant parent genotypes would likely have low fitness. Only specific combinations of parental genomic contributions may produce viable, intra-fertile hybrid species able to accommodate potential constraints arising from intragenomic conflict. Second, ecological conditions (competition, geography of the contact zones or the initial frequency of both parent species) might favor different outcomes ranging from sympatric coexistence to the formation of hybrid swarms and ultimately hybrid speciation. Finally, history may also play an important role in promoting or constraining recurrent HHS if multiple hybridization events occur sequentially and parental divergence or isolation differs along this continuum. We discuss under which conditions HHS may occur multiple times in parallel and to what extent recombination and selection may fuse the parent genomes in the same or different ways. We conclude by examining different approaches that might help to solve this intriguing evolutionary puzzle.