We are using the Creative Suite 6 Production Premium. Different employees want to use different components from the suite. Is it therefore possible to install and use components from the suite on different computers in the company?

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No, Adobe does not allow that. According to the EULA all products from one suite may only be installed on the same computer.

Source: Adobe EULA as of Juli 2016

Lizenzvertrag_Adobe_Stand-Juli-2016Download