Repeating texture at different sizes

I'm creating a Voxel Game based on a Octree data structure. For texturing I'm using a spritesheet texture (not the Unity one), which I'm adressing using uvCoordinates. Is it possible to scale my texture at different resolutions and make them repeatable? To achieve it I'd neither like to create additional triangles nor use a separate texture for every block type.

To give you a better understanding of what I'm trying to say here are some screenshots:

That's how it looks like currently:

And how it's supposed to look (for this screenshot i disabled octree merging):

Thanks in advance!