One purchase of PT3 gives you a license valid for use on up to two machines that you own and operate at once. If you want to use it on a third machine you'd have to buy a second license. However, you can uninstall and reinstall the software as many times as you'd like, so if you uninstall from machine A you can then install on machine B and it's still just one "slot".
PT3 by default creates a database on your machine that is not linked with any other machines. If you have one central computer that you would like to run the database, though, you can do that and have all other machines using that database. (You shouldn't import into the same database in multiple locations though, that could cause corruption.) For more on how to network a postgresql database, see
this tutorial.