Yes, from what I understood you could order the accuracies that way.
I can try to comment more if you provide more detail of the 3 steps, e.g., is it easy to write the formulas
(e.g., step one looks like you solve (1) A_h x_1 = b_h where A_h and b_h are probably in FP16; after that
is explicit update like x2 = x1 + something, so if you are improving (1) would the term “something” be some
residual, maybe preconditioned for (1), similar to the iterative refinement and maybe done in single precision, etc.?).