Short answer: No, I do not believe one setup would do both types justice.
One has to start from the premise of what is a given speaker design is assuming the listener wants. An omni delivers the enveloping sound from all the room reflections it energizes, and in the right room MBLs can be spectacular, especially when reproducing instruments that naturally light up a room acoustically, such as a grand piano. But the room is always 'coloring' the sound to a significant degree. Treatments to tune or focus the delivered sound-stage involve diffusion and selective absorption along front and side walls.
A stat (or any line source dipole) is about delivering the benefits of low-distortion line-source focused energy. The penalty is it's dipole, radiating equal amounts to the rear, managing the rear wave is critical to getting the best out of a Stat. So room treatments of the walls behind the speakers are critical in my experience.
I've spent more than a decade tuning my room (using measurements) and arrived at a satisfying result, but it took tremendous effort and tons of treatments and gear to achieve it. It's now perfect for large stats, but I would not imagine an MBL 101 sounding its best in my room.
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