How do you put textures onto tiled ground texture?

Let's say you have a street that is just a tiled tarmac texture. If you wanted to put some potholes in the street and manhole covers, how might someone go about this?

I'm currently just overlaying quads (which is a basic 2-triangle plane) on top of the street, but I can't align it too closely to the street or I get weird artifacting, and I can't bring it away from the street too high or else the player's feet disappear into it and it's quite obvious to be levitating. So I just need to balance it as best as possible? I guess I just want to make sure there's not a more standard solution I'm missing out on here. :)