I mean, I can conceive of level visual designs that might intentionally use both together in the same level, like maybe one side of the level is where your normal lemmings enter and gathered in, and the other side is zombie-lemmings infested, and a suitably palette-swapped set of terrain pieces (and maybe even objects) used to depict the zombie side differently from the non-zombie side (eg. maybe grayscale for the zombie side).
But on the whole, I expect such mix usage to be relatively rare.
That said, perhaps the level file format could even be extended to support applying per-element palette swaps, meaning in extreme case every single individual piece of terrain and object in the level can each have their own independent palettes/recolors. In practice going to such extreme direction should be rare and perhaps somewhat discouraged (I imagine it might increase memory consumption, especially for objects), but in theory one could consider implementations along those lines, and then it would certainly allow level designers to use same style with multiple palettes applied all within same level.
Even the extreme case I just mentioned might not actually be so crazy design-wise, though again probably not common. So maybe not literally tweaking every single terrain and object pieces, but imagine a vertical scrolling level where visually, you want to depict the lighting being the brightest at the top and darkest at the bottom, as if the lemmings are descending deep down into a cave or the abyss starting from near the surface. The cleanest way (but not actually achievable currently, I think) to do this is to apply a single continuous gradient of opacity, overlaid over the entire level area. But an alternative approximation of same effect could be to recolor each terrain and object to be brighter/darker based on their vertical positioning.