You can if the community developers give you permission (licenses) to keep offering the whole project under both open and commercial terms. Happens all the time.
Many companies use contributor license agreements for this. Others simply ask that community contributors make their work available under permissive terms like Apache, MIT, or BSD.
If, like QT, the library is your whole product and you do not depend on the community for contributions, then GPL is great. It forces vendors of non-GPL software to acquire a commercial license, while open source projects can use your product without restrictions.
If it is not your core product and you want to encourage community contributions, BSD and MIT might be the license of your choice. You cannot prevent other companies from using the software, but neither are you prohibited of using any community contributions in your product.
When using the GPL, it comes at one huge disadvantage: you cannot accept community patches to the GPL software and use them for your closed-source branch. This is the incentive for companies, to use a more permissive license for some of the software. They can reintegrate community contributions into their closed software product. Of course, this only works out, if the closed software product adds significant value over the open sourced part, or no one would buy it.