You can, you just have to watch which perl you're using. Only one can be "first" in your PATH. For this, I'd suggest leaving the old perl as the default, primary one. This will have the least effect on existing (production) code.
You can, however, have a secondary perl in your PATH with a different name. For example, perl5.22.2.exe could be in your PATH, and you can use it when running your tests.
If you have a batch file or similar as a wrapper around perl scripts, you can have the batch file for each app run the correct perl for that application, and you merely need a) a way to override the perl it uses, and b) to have it default to the tested level of perl you want it to use. That way you can test with 5.22.2 for a while, but the default remains 5.10.1. And then you can switch the default over to 5.22.2 when you're ready for that application to switch.
Whether it's client-side or server-side doesn't make any real difference to this.
(And platform doesn't make much difference, either - while the actual implementation on a unix/linux system might be a bit different, the general idea doesn't have to be. You can have both installed at the same time, and manage which perl to use on an application by application basis if you have to.)