Very often, the reason why this happens is related to a cluttered global environment. In Julia, you can never have two different versions of the same package loaded – however it is possible to have multiple versions of the same package installed.
You normally create local environments for your different projects. For more information, see this short introduction or the official docs.
In each environment, you can install the latest compatible version using ] add Package, a specific version ] add Package@v1.1 or even a specific tag or branch (i.e. a a non merged PR for some package) ] add Package#pr-branch.