Auditor Qualification

When we partner up with a vendor platform usually they bring up their own qualified partner auditor for the audit, where their team sits with the auditor for conducting the audit and keeps us out of the audit process.

To conduct a SOC 2 audit, an auditor must be a licensed Certified Public Accountant (CPA) from a firm accredited by the American Institute of Certified Public Accountants (AICPA)

So if we manage to bring an auditor at lower costs who is a lisenced CPA from a firm accredited by aicpa, and then conduct the audit we can save up. - again- will the platform vendor allow this ? if yes what all support will be cut down ?, will their team go for the audit representing us? will the process remain smooth?