I want to recolour an object to have a normal version and a grungy-looking version. Can I add a texture with a degree of transparency and make it load on top of the normal texture, maybe? Or do I really need to make two separate versions? Sorry if this has been answered somewhere, I tried Googling it but only got results for TS4

You can make two different recolors of the same item, one grungy and the other regular. Wouldn't that do the trick?

TS3 has this option (CASt, with patterns/colors + overlays). TS2 doesn't. If you want to use any type of overlay for a mesh, you'll have to edit the mesh, which usually means adding to the polycount.

Sure, I'm just curious about whether can object can have different texture layers, maybe even something that can be triggered in response to game events (like how Maxis objects often become dirty or sooty)

Feenwald did something similar with these rugs: http://www.feenwald.com/en/deko/tep_bb_01.php
It's just an added subset + mesh part with the fringes and overlay, and there's an invisible version (I think?) for the overlay. I've done similar things, and in some cases it's the easiest way to create more options, but it depends on the object. That one is (I'd think) because it's repo'd to Jonesi's blankets, and it's the only way to add extra fabric texture. I would not recommend doing it with anything that's got a lot of polys, though. It also takes up a recolorable subset, so you're stuck with one for colors/patterns.

The easiest is to just make double the number of recolors. You can make one transparent overlay texture that you can slap onto the rest of the textures. That makes the recoloring a lot easier.

I don't know if you can code it into the item somehow, but I have some doubts on the ease of things. The item would need to have some form of wear-and-tear option (thinking of teddy bears, but he worn state is kinda broken without a mod that fixes it), plus regular items that have a "dirty" state (counters, highchairs, and similar) that sims can clean. I have no idea how to mod this for objects that don't have it to start with, though. The ones that do have "dirty" or "worn" states usually come with extra texures added, so it's just the matter of replacing them.