Decidability of the universal algebra consistency problem of the bi-unary signature

Question

This is yet another follow up to my previous question on universal algebra and decidability of consistency, here: Follow up to a previous universal algebra question on decidability of consistency. In that question, I was told that the consistency problem for the special case of the mono-unary signature $\{f\}$ is decidable. Now, what if we add another unary operation to the signature, to get the bi-unary signature $\{f,g\}$. Is that still decidable? If so, how many further unary operations in the signature are enough to make the consistency problem undecidable? Surely, there has to be some finite number of unary operations which make the consistency problem undecidable, right?