TestStand Development licenses are either user-based or computer-based.
In the case of a computer-based license it can only reside on a single PC. In this case anyone using that PC can use the license. Using this license on multiple computers is breaking the license agreement. Unless you deactivate it on the previous computer. So essentially, you can move it from PC to PC but it can only be activated for one PC at a time.
User-based licenses, according to NI agreement, can only be used by an identified user of the license. They can be installed on a desk PC, lab PC and home PC (but only for work use). As with the computer-based license you can declare different lab/desk/home PCs, but technically only 3 at a time. All others should remain deactivated.
You can move a license between user-based and computer-based if you want but you have to follow the rules for whichever you declare the license to be.
All that being said, it is completely on your honor, as far as I've seen. NI could prosecute if they found you breaking the rules but they don't seem to be interested in policing that in my opinion.
So yea, go ahead and install TestStand on all the computers you want. Just deactivate and activate licenses according to the rules above. Having the engine on the PC is not a crime.
DISCLAIMER: I do not represent NI, nor do I work for, or speak for, them in any way, shape or form. You should read your license agreement for a more definite answer. This is just my interpretations of what I've dealt with historically.
Cheers,
