evolution - Is there a theoretical maximum on the number of sexes a given species can have?

Background: To the best of my knowledge, most sexually-reproducing species of organism have two sexes, although there are also sexually-reproducing species of organism (flatworms come to mind) which have only one sex. (Depending on one's definition of sex.)

Many species of fungi are both sexually reproducing and apparently have more than two sexes. (Depending on one's definition of sex.)

There are also species of lizards with more than two biologically determined "gender morphs". It is even more debatable than in the case of fungi whether these morphs should be considered separate "sexes" or not, since their mating compatibility network is bipartite.

Question:
Is there a theoretical maximum on the number of sexes a given species of organism can have?

Elaboration: There would also be a lot of different possibilities -- already with three sexes, one can imagine at least two different means by which sexual reproduction could occur -- any one of three combinations of two individuals from two distinct sexes (most likely in "rock-paper-scissors" fashion), or the combination of three individuals from all three distinct sexes.

How, for example, might either of these two scenarios be maladaptive compared to sexual reproduction of two individuals in species with two or fewer sexes?

I am asking about species with more than two sexes/mating types in general, not necessarily about situations where more than two sexes are involved in a single reproductive event. (Contrast with this related question.) I am also not restricting to animals, or even multi-cellular organisms, or even eukaryotes, since these restrictions might affect the answer. (Contrast with this related question.)

Note that this answer to the second related question implies that we should expect the mating compatibility network of anisogamous sexually reproducing organisms to be bipartite. But note that, as in the example of the side-blotched lizards, this doesn't necessarily preclude having more than two sexes, nor does it give a theoretical maximum to the number of possible sexes. And since I don't want to necessarily restrict to anisogamous sexually reproducing organisms (i.e. isogamous ones would also be fine), then that answer also does not provide a theoretical maximum for isogamous sexually reproducing organisms either.