Can you add a texture and a spritesheet on same object?

I want to texture an old computer. However I was wondering can I make a sprite sheet to animate different things on the monitor? Or will I need to separate the monitor screen from the object?

You can use the Decal shader: it accepts a base and a decal texture, thus you can paint the monitor with the base and change the decal texture to show different images - but the uv mapping is the same (except for tiling and offset), thus it must be carefully defined.

A simpler alternative is to child a suitably sized plane to the monitor - a little ahead of the monitor screen to avoid Z fighting - and paint it with the images