The KPZ universality class is expected to contain a large class of random growth processes. In some of these models, there is an additional structure provided by multiple non-intersecting paths and utilisation of this additional structure has led to derivations of exact formulae for the distribution of quantities of interest. Motivated by this we study the multi-layer extension of the stochastic heat equation introduced by O'Connell and Warren in [OW11] which is the continuum analogue of the above mentioned structure. We also show that a multi-layer Cole-Hopf solution to the KPZ equation is well defined.