Adding a Third Partner to Our Self-Funded Search - Pros and Cons?

Hi everyone, My partner and I are both ex-PE professionals currently running a self-funded search. We’re considering bringing on a third person - a friend of my partner’s with a strong private equity background - to help manage the growing workload and eventually divide responsibilities post-close (across ops, finance, and M&A). I’m curious if anyone has experience running a search with three partners instead of two. Besides the obvious dilution, what pitfalls should we be aware of? Are there advantages to having a third person that we might be overlooking? Would really appreciate any thoughts or lessons learned. Thanks!