Jack of all trades master of none.
There is no such thing as a universal film. Each has pros and cons.
To accommodate the different lighting conditions, you need to accept that you will need to use more than one film.

I use ISO 100 film as my standard film for outdoor shooting during daylight, for the exact reason you mention. 400 speed film would almost max out the controls on my camera at f16 @ 1/500 sec, leaving me with very little to no exposure control.

And indoors, besides pushing the film, use FAST GLASS, like a f1.4 lens. I learned the hard way, that pushing film with a slow lens will not make up the light lost by that slow lens. There is image quality reduction when you push film.