Today I had an executive ask me is there is any industry data on how many projects a Performance Consultant can support at any one given time.
Can anyone lead me to any data that discusses Performance Consultants capacity to support projects? Thank you in advance

It depends - must depend - on the scope of the projects and how involved one needs the consultant to be. It's up to the consultant to say "stop - I cannot take anything else on my plate."

SSFN has it spot on. The Robinsons (before their retirement) used to collect this data. Off the top of my head, it varied from 4 projects a year to 25. That is because...
1. The role of the consultant varied. In some cases the PC would hand the project off to ISD or trainer or OD or HR types but still participated as a coordinator. I've consulting with companies where their "performance consultant" was really just a trainer. Others where the PC just did FEA and client liaison. Others where the PC was a major POC for clients (and spent a lot of time holding hands and conferring with).

2. The size of the project varied. Obviously a project where we have to design new appraisal targets for one executive has a different time commitment than one that involves designing and rolling out a new OJT training scheme for 3 shifts at the factory involving 850 employees.

3. Depends upon how you define "project." Not to get too nit-picky here but in some cases, a project is "a letter of agreement with a client that we'd like you to look into issue X." And no work or improvement might result from this, it's just a handshake and commitment that "maybe X is a problem and some info could be useful." Or "project" could mean "intervention" (as in, a defined problem with agreement and resources committed to acting). This is less of semantic difference than you'd think. Imagine you spend 3 months prepping some work and the client or organization pulls out the budget on it. Does that mean you spent your last 3 months on "nothing" (because nothing was implemented so there was no "project")?