Mostly the answer is No; you won't run into problems.
Do note some desktop environments are written & only reliably work with specific (including a single) window manager. LXQt is one desktop that is WM agnostic as the LXQt team put it, ie. it'll work with any.. but not all DEs are tested, nor designed to work with any WM
I really like Xfce, and recall using ~6 WMs with Xfce (but note I won't have tested all WMs with it; I have 5 only currently installed & usually only use 4 in QA)
I'll also add I've probably only tried 3 with GNOME (with most my testing related to openbox
& GNOME).
Also note that the features you may expect to work in a DE can change how they operate when you change WM. Again using LXQt as example (I'm a Lubuntu team member thus know it probably best), Lubuntu code their additional features they add to LXQt specifically for openbox
, so if it's replaced - you lose those coded openbox
hotkeys etc.. thus the experience can change when you change WM, but the DE still works (just may not be identical due to WM change)
You can install extra WMs via a simple
sudo apt install fluxbox
to install the fluxbox
WM... likewise blackbox
etc... That doesn't change how they interact with specific DEs, nor consequences when a DE is made to work with WM. That will install the fluxbox
package & WM to your system, but it won't be used until you login [with it] or tell a desktop to use it... ie. Xfce & GNOME will happily ignore the package as they're not configured to use it.. You can select it at login (ie. use fluxbox
alone without DE), but again the DEs you have need to be told to use it. Xfce of course is intended to be used with the xfwm4
WM (the WM of the Xfce Project) though Xfce allows that to be changed.