How to set float or float4 UV in Mesh.

Hello. I'm trying to create a shader that supports an outline. My approach is to assign barycentric coordinates to each triangle of a face. These are 3 dimensional.

I know Unity's UVs support float3 or float4. Is there a way that I can pass that to the Mesh? If not, do I have to create my own Mesh-like data structure that communicates directly with the shader?

Thanks!