Spectral sequences to involve together two ideals of a ring

Question

I'm looking for spectral sequences to involve together two ideals of a ring. For instance, let $I,J$ be two ideals of Noetherian ring $R$ and $M$ be a finite $R$-module then we have the following spectral sequences $$H_I^i(H^j_J(M))‎\Rightarrow‎ H^{i+j}_{I+J}(M).$$ $$\operatorname{Ext}^i_R(R/I,H^j_J(M))\Rightarrow‎ \operatorname{Ext}^{i+j}_R(R/I,M),\quad \text{if}~~ J\subset I.$$