To answer the question - can too many UX designers spoil a design - the answer is of course, they can, but they don't have to.
Any UX designer capable of understanding the needs of the user and applying the business rules to a project, while collaborating with everyone involved, but who then screws things up due to an inability to work with someone right next to them is simply not doing their job - for themselves, for their client or company, or for UX as a whole.
Think of it like combining electrical phases. You get two people out of phase with each other - they cancel themselves out. You get two people in phase with each other - they double their effectiveness.
However, due to the nature of the field of UX, and it's need to consider end users, then UX designers are more likely to be in phase with each other than some other members or roles within a group.
Whenever possible, I like to bring up Damien Newman's squiggle of the design process which indicates how the design process starts off in a messy research phase, narrows through the design prototype phase and settles down to an almost flat line as a design solution is reached.
Multiple UX designers have more scope for exploring more of that huge research space, and will have more diverse input as a result, but this should still all come together to a shared vision, not just with each other, but with the whole team and with all stakeholders.
And it's exactly because of the whole collaborative effort that multiple UX designers should be able to enhance a design rather than spoil it - because they are not doing it for themselves.