Maximum Equal Sum K Subsequences
This problem is NP-complete by reduction to the given subset sum problem, which asks if there is a subset $S$ from a set with a certain sum $n$.

Suppose we are given such an instance and that your problem can be efficiently solved. Then we can transform the instance by making $S' = S \cup \{x, x - n\}$ for some sufficiently large $x$ and solving your problem to find the $K = 2$ maximum equal subsequence sums. Then iff the answer includes $x$ and $x - n$ there is a subset that sums to $n$ and we efficiently solved the given subset sum problem.