I would say that it depends on how the core and addons are attached and how the core is licensed.

If the core is a library, and licensed under LGPL, the proprietary add ons can dynamically link to it without issue. You could take community contributions. This would not be true if the library was GPL. Anything that links to GPL has to be GPL compatible (make source code available).

If the proprietary addons are libraries and the core links to the addons, the users could violate the GPL when they link to them, unless you as the original author of the core, specifically enumerate the addons in the license you distribute to them. You would not be able to take community contributions in this case.

If the core communicates to the addons without adding the addons to its assessable region, such as talking over pipes or sockets, you would have no licensing issues even if the core is GPL and has taken community contributions.