What is known about irreducible decomposition of tensor products of (infinite-dimensional) unitary irreducible representations of $SU(2,2)$ (or, more generally, simple groups of split rank greater than $1$)?

I am aware of some general and special results for split rank 1 groups, but I feel that the case of split rank 2 should be considerably more complicated. For example, I believe I can construct infinitely many (more precisely, continuous families of) kernels which at least naively appear to be singlets in a tensor product of any three principal series representations for $SU(2,2)$. This seems to suggest that some multiplicities in the decompositions are going infinite.

admissibleirreducible representations only the groups $SO(n,1)$ have finite tensor product multiplicities. If you are interested I could try to find references. $\endgroup$