Can test flights carry passengers?
Flight tests of new aircraft are covered under Part 21 Subpart B—Type Certificates §21.35 Flight tests.

There is no provision for the carrying of 'passengers' during any test flights, but then, there is no limit on the number of 'flight crew' either. FAA regulations does not explicitly prohibit the carrying of any passengers as such; however, it places onus on the applicant for ensuring the safety of anyone abroad during test flights:


  (d) Each applicant must show for each flight test (except in a glider or a manned free balloon) that adequate provision is made for the flight test crew for emergency egress and the use of parachutes.


This places severe restriction on carrying of anyone during test flights. However, before certification, the manufacturer can carry passengers as long as it is not for commercial purposes. Actually, Airbus did this during the test flights of A350 XWB:


  Another important aspect of A380 and A350 XWB testing was the Early Long Flights (ELF) programmes, which went above and beyond certification requirements. For these evaluations, a cabin-equipped flight-test aircraft was operated on simulated commercial services with real “passengers” – comprised of Airbus employees – and actual airline flight crews to evaluate cabin systems in typical operating conditions.


Unless the flight testing is at an advanced stage or the manufacturer is extremely confident of the design, I don't see any non-essential flight crew being allowed in test flights, for obvious reasons.

In case of test flights after maintenance or alteration, CFR § 91.407 - Operation after maintenance, preventive maintenance, rebuilding, or alteration says almost the same thing:


  (b) No person may carry any person (other than crewmembers) in an aircraft that has been maintained, rebuilt, or altered in a manner that may have appreciably changed its flight characteristics or substantially affected its operation in flight until an appropriately rated pilot with at least a private pilot certificate flies the aircraft, makes an operational check of the maintenance performed or alteration made, and logs the flight in the aircraft records.