Centrist party in a multiparty system?

Let's discuss a hypothetical situation: America ditched FPTP duopoly for a proportional multiparty system. Both the GOP and Dem split up into 4 smaller parties: far-right GOP, centre-right GOP, centre-left Dem, and far-left Dem. At the same time, old parties can expire and new parties can take their place.

With that said, is a centrist party possible in the new system, where the party holds several views and elements from both sides but remains in the centre? Why or why not? And if they are the alternatives to both sides (which now have 4 rather than 2 parties) would you identify and vote for this party?