i) A stock objection to the Protestant faith is the proliferation of denominations. Sometimes this involves the specific allegation that sola Scriptura is self-refuting. We need something outside Scripture itself to determine the boundaries of Scripture. I've addressed that objection on more than one occasion. For instance:
ii) Mind you, that objection overlooks the intertextuality of Scripture. The case for the canon of Scripture isn't confined to external evidence.
iii) But let's move to a new point: if the multiplicity of denominations is a problem for the Protestant faith (which I don't concede), it's no less a problem for Catholicism.
To begin with, a multiplicity of denominations is only essentially problematic on the assumption that there is one true church to which all Christians ought to belong. But of course that assumption begs the question in favor of Catholicism. If, however, there is no one true church, then there's nothing intrinsically wrong with having more than one Christian denomination (or independent church). So the Catholic objection only has traction on the assumption that the church of Rome is the one true church. But that's the very issue in dispute!
After all, the NT itself can speak of the church in both singular and plural terms. One church and many churches.
iv) In addition, even assuming there's one true church, the church alone can't determine what's the one true church, for this involves a comparison between rival claimants to that distinction. The one true church can't be the standard of comparison for determining which candidate qualifies, because you first need to determine which candidate is the one true church before it could be the benchmark. In a contest between ecclesiastical competitors, you will need an extra-ecclesiastical criterion. An aspirant can't very well be the referee.
Ironically, when Catholics object to sola Scriptura, it's easy to contrast a parallel concerning the one true church. When there are two or more contestants for that honor, you need an extra-ecclesiastical tiebreaker. Something over and above the church to point to us to the rightful claimant.
Even if there were one true church, you don't have access to that criterion before you establish which claimant is, in fact, the one true church. At best, that's something you can only adduce after the fact, and not in advance.