Is it possible, for instance, to run a Shimano Nexus IGH with front derailleurs, to have even greater range of gearing, while gaining the advantages of IGH (low maintenance, stationary shifting)?
It's possible in the sense of yes you can set up a bike with an IGH, a sprung chain tensioner, and a front derailleur, and the bike will go.
Internal hubs have limits in how much torque can go through them without breaking, and by sizing down the chainring you begin to push those limits. Here are what Shimano and Rohloff say about it: (From the Rohloff Speedhub instruction manual) (From the Alfine dealer manual, DM-SG0004-06)
You'll note that Rohloff spells out loud and clear the limits are to prevent "overstraining" the hub while Shimano is more opaque. So it goes. The limits are also specified independent of wheel size, which as far as I can tell doesn't make any sense because the distance from the axle to the ground is the lever arm pushing back on the hub, but it gives you an idea if you assume the numbers are for a 700C trekking application, which is the largest single market for these hubs in the world.
Those charts are approximate because they're making assumptions about the power input of the rider, so a lighter rider has more license to do what you propose.
The short answer is that you probably shouldn't add a front derailleur to an internal hub for the main reason one would ever consider doing it, which is to get extra low gears for something like a cargo application while still having the robustness of an IGH. If it's just for science or some other application where it's okay if maybe the hub blows up someday, it's fine.