In theory, this should be no problem.
You'd probably want each of the response pads to be programmed with different outputs for their buttons. That way, you'd know which subject answered a particular question.
Unfortunately, I'm not personally familiar with any hardware of this type. However, if you're considering a particular system, let us know. We can look at the appropriate documents and determine whether it will be compatible with MediaLab / DirectRT.
FYI, any system which outputs data in a simple serial (rs-232) stream should work just fine.