If the parties have stable factions and their internal elections are FPTP, then sure. The two right-wing factions of the British Labour party just rolled over the party's left-wing by running a joint slate of candidates while the left slates split the vote.
Having said that, electoral politics within parties doesn't tend to be as important as other things: bureaucratic control of the party machinery, for example.
Having said that, electoral politics within parties doesn't tend to be as important as other things: bureaucratic control of the party machinery, for example.