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There are no issues with having multiple versions of PD installed on the same computer. Just remember that if you create a new project in PD20/365, or if you open a project made with PD13 and save it in PD365, you won't be able to open it in PD13.
francis1954, the answer depends on which version of the software you had purchased. If you bought an upgrade, the EULA which you acknowledge during installation clearly states:
UPGRADES
If this copy of the SOFTWARE is an upgrade from an earlier version of the SOFTWARE, it is provided to you on a license exchange basis. Upon your installation and use of this copy of the SOFTWARE,
you agree to voluntarily terminate your earlier EULA and you will not continue to use the earlier version of the SOFTWARE or resell or distribute it to another person or entity.
However, if you bought the Full new user version instead of the Upgrade version, you can keep both versions of the software and not violate the EULA which you accepted.
Jeff