We are developing an automatic machine learning software for researchers under a GPL license. This will allow them to use different ML algorithms on their data. Is it possible to offer an additional proprietary algorithm as a plug-in for a fee? The application wouldn't depend on the proprietary plug-in, neither they would be included in the base bundle and would be downloaded separately.
If the code is all yours, you can do whatever you want. If it is based on/includes other GPL code, you must distribute under GPL or you aren't allowed at all to distribute the result.
GPL code to be combined with closed plugins goes against the spirit of GPL, so that makes not much sense. But you certainly can add a special dispensation to use closed plugins using the public interface to your code. Murky, to say the least.
Check out the LGPL, it might be nearer what you want (it allows linking to closed source).