This is probably a huge reasoning error, but wouldn’t you “expand away” with the expanding away part of the universe at the same rate, sort of riding along with

This is probably a huge reasoning error, but wouldn’t you “expand away” with the expanding away part of the universe at the same rate, sort of riding along with the expansion given that c is the same in the point of reference (the expanding away faster than c part)? n.b. I obviously lack the vocubulary to communicate properly about this, help needed!