Is there an analogue to spectral sequences where, instead of chain (bi)complexes, we use simplicial sets?
Namely, let $\{\mathbf{S}_{p,q}\}_{p,q}$ be sets such that $\mathbf{S}_{p,\bullet}$ and $\mathbf{S}_{\bullet,q}$ are simplicial sets (for all $p$ and $q$). Would it be possible for example to recover information on the homotopy of $\mathbf{S}_{p,\bullet}$ knowing the homotopy of $\mathbf{S}_{\bullet,q}$, or more generally what information about the first simplicial set is possible to obtain knowing something about the second one?