Is it possible to set different textures and/or UV maps for the same mesh? I'm part of a small programming company, and we're designing assets for our first game. My assignment at the moment is to texture this mesh:

I had to look up a few tutorials on how to do this as I'm still fairly new to Blender(as well as game design), but after a few hours, I managed to construct a decent UV Map.

Now, here's where I start to run into a problem. Most of the mesh is separated into different islands, but once I start to do some texture painting, I select the faces I want to color using the bucket tool, and somehow the colors overlap onto other islands.
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I'm thinking this has something to do with the fact that each island in the UV Editor is relatively close to one another(and also that I have the bleed factor set to 5 pixels), but it also raised a question: is it possible to assign multiple textures to the same mesh, and if so, do I have to make separate UV maps for each texture?
Basically, what I want to do here is create separate texture images for different parts of the same mesh. Like for example, I need one image for the walls of the arcade machine, and then another for the joystick and buttons.
I apologize if this has been asked before. I searched the web for an answer, but I couldn't find a solution that fit my needs.
Yes, you can layer multiple textures with multiple UV maps on a single object. Here I have a project from last year in which I did so. For this example, we'll look at the stitches ontop of the leather texture.
On the left is my default (base) UV map for the main texture. I've highlighted the strip where the stitches go so you can see how it changes on the next UV map.

To create a new UV map, simply click the &quot;+&quot; in the UV Maps section in the Object Data Properties Panel. Here is the second UV map for the stitches. As you can see I've straightened the UV islands. I've also shrunk down the rest of the UV's I don't need so they are out of the way (that's the black spot on the bottom right corner).

Once you have got these two UV maps, you'll need to load the node editor to combine the two. Here is my setup to combine the stitches and the leather:

You'll start with your Principled BSDF and Material Outpode node. Drag in the two image textures you plan to use and connect them to a MixRGB node (displayed as just Mix) as shown. Connect the Mix node to the Base Colour input on your Principled BSDF node. Finally, create an UV Map node, and edit its value to be the name of the UV map you want to layer on (not your base UV). Connect the UV output to the Vector input of the image to layer on.
I believe for the texture you layer on, you'll need to save it as a .png with everywhere except your texture being transparent.