I have a stack of 96 well plates containing lysates in RLT Plus. I dont want to process them all at once, rather a few wells per plate to start. Will re-freezing the rest of the plate damage the samples?
Of course freeze/thaw will negatively affects cells/proteins and DNA integrity. However, this depends on the properties of your proteins and the kind of test you are going to perform. If you are using a commercial kit, I would suggest contacting the manufacturer to let you know the. maximum number of freeze thaw cycle that your sample can tolerate
You may want to consider the fact that in RLT most macromolecules are quite stable. Even for RNA isolation individuals in my lab frequently leave samples in RLT at room temp for extended periods without any negative impact on their experiments. So given your circumstances, freezing and thawing your samples again may do more harm than good.
For a couple of days I would also recommend to store the samples in the fridge (4°C) rather than freezing them.
If you need to freeze them (what is not a problem per se), think of freezing them in aliquots, so that you won't need to repeatedly twaw/freeze the samples for subsequent analyses.
For long-term storage (e.g. for years), especially of sensitive molecules like RNA, to my experience it is better to freeze the (well) purified samples.
Normally buffer RLT is appropriate for long-term storage at -80C and if you can add RNAse A into the buffer so you can precent the degradation of you RNA. In my personal opinion, if you add RNAse each time you thaw your sample you may keep your RNA intact, while lysing your cells.