We show how, starting from a mapping where the independent variable advances one step at a time, one can obtain versions of the mapping corresponding to a multi-step evolution. The same procedure is applied to discrete Painlev{\'{e}} equations and we proceed to establish Miura relations between the single-step and the multi-step versions (in the present study "multi" referring to double, triple and quintuple). These Miura relations are discrete Painlev{\'{e}} equations on their own right. We show that, while in some cases it is impossible to obtain a multi-step equation for a single variable, deriving a Miura system is still possible. We perform our analysis for equations associated with the affine Weyl groups E8(1), E7(1), E6(1) and A4(1).