Yes, you could put a resistive and a capacitive touchscreen one on top of the other. (It would have to be capacitive on the top, resistive underneath.) But although that would give you the best of both worlds in terms of capabilities, it would be the worst of both worlds in other respects.

Either sort of touchscreen has two layers of a transparent conductor. A resistive touchscreen has two "solid" layers on separate pieces of glass or plastic, with spacers between the two so they don't come into contact unless pushed. Pushing down on it with a stylus brings the two layers into contact. How does this suck? Let me count the ways. 1. Lots of layers. ITO isn't perfectly transparent, and glass/air interfaces are always going to reflect a bit even with anti-reflective coatings. So you lose transparency (by different amounts at different wavelengths too, so either you get a wrong colour balance or you lose more brightness to fix that up) and get more reflections. 2. Poor robustness. Your front sheet of glass or plastic has to be thin enough to flex, and you're flexing it all the time. That's not great. The ITO layer on the front sheet is also flexing, and that's even worse because you want it to be thin (for optical performance) but the thinner it is the more readily it cracks. 3. Thickness. Multiple layers of glass or plastic, physical spacers in between, ugh.

Adding a capacitive sensor to this will make the optical quality even worse because you'll need more ITO layers. What's more, the capacitive sensor will have to be on the top (I think trying to do capacitive sensing through the conductive layers of a resistive sensor is a non-starter), which means those ITO layers are also flexing when you push on them, for extra-bad robustness. And you'll probably need to space them away from the resistive sensor underneath a bit, making the sensor assembly even thicker, though perhaps there are ways around that.

Perhaps you could combine one layer of the capacitive sensor with one layer of the resistive one, but that seems tricky. A typical capacitive touchscreen uses two layers of patterned conductors, with lots of gaps in (so much so that although there are two layers, over most of the display only one is present, at least in the designs I know about -- it's been a few years since I was in the business, so technology may have moved on). A typical resistive touchscreen uses two solid layers, and putting gaps in them will make it completely fail to work. I wouldn't want to rule out the possibility of combining them, but it would be tricky.

Well. Actually, there's another design of capacitive touchscreen which uses a single solid conducting layer a bit like one layer of a resistive sensor. It's much harder to get good accuracy that way, but I've seen sensors of that design of tablet size and larger. You might well be able to combine that with a resistive design, but I bet the accuracy would be poor.

(And, incidentally, using a resistive sensor with a stylus "for fine input" doesn't seem like such a great idea to me, for the same reason: it's difficult to get really good accuracy from a resistive sensor.)

There's another simpler approach: use just a capacitive sensor, and a conductive stylus. That has some accuracy problems of its own, especially if the sensor wasn't designed with stylus use in mind, and it won't enable you to use the device while wearing gloves or a wetsuit or whatever, but it seems likely to be a much better compromise than stacking one sensor on top of another.