In 1974, Gugenheim and May showed that the cohomology $\Ext_A(R,R)$ of a connected augmented algebra over a field $R$ is generated by elements with $s = 1$ under matric Massey products. In particular, this applies to the $E_2$ page of the $H\FF_p$-based Adams spectral sequence. By studying a novel sequence of deformations of a presentably symmetric monoidal stable $\infty$-category $\cat C$, we show that for a variety of spectral sequences coming from filtered spectra, the set of elements on the $E_2$ page surviving to the $E_k$ page is generated under matric Massey products by elements with degree $s < k.$