I'm not expert enough to say if there will be long term damage but I've done it many times with server PSUs, before you do anything though you have to make sure you won't have a ground loop. Most of these PSUs have the output negative tied to case and wall ground so you have to disassemble them and isolate the them, normally this means disconnecting the output ground from the case but every PSU will be different and I'm sure some you can't easily disconnect them. That being said I can't recommend doing this, they are really not designed to be operated in series and the isolating thing is a bit of a hack so this may be one of those do as I say not as I do situations, at least unless you really understand what you are doing.
Edit: Also should wait on someone more expert than I to chime in here.