Multiple textures on one triangle

Hi! I'm fairly new to shaders and uv-mapping and game programming in general. I wanted to implement Dual Contouring or Dual Marching Cubes to display voxel terrain. Dual Contouring creates one quad for every voxel, so I can put in uv coordinates and a texture atlas to display if the voxel represents grass or stone or whatever. But Dual Marching Cubes creates huge triangles (for example on a flat area), combining many voxels into one quad (and triangle). Can I somehow still show grass and stone textures on a single triangle to represent underlying voxels?

I hope you get my question :) Can this be achieved with a shader or something? Thanks a lot! Have a nice day, Minja