Normally what researchers do in this kind of situation is create multiple experiments (either different or identical depending on the need) and use the subject ID as a merging variable later (e.g., in SPSS). So, generally, yes, this is not a problem. It gets a bit more complicated if there are contingencies that need to be carried from one session to another. Say a subject scores high in self esteem during session one which, in session three, will mean he or she gets some measure intended only for high self-esteem subjects. That kind of stuff can also be accomplished but it's a bit trickier.