We prove a “twist-compatibility” result for p-adic families of cohomology classes associated to symmetric spaces. This shows that a single family of classes (lying in a finitely-generated Iwasawa module) interpolates classical cohomology classes of many different weights, including twists by Grössencharacters of possibly non-trivial infinity-type. This subsumes and generalises a number of prior results relating to Euler systems and p-adic L-functions, and we conclude with some novel applications to Euler systems for \({{\,\textrm{GSp}\,}}_4\) , \({{\,\textrm{GSp}\,}}_4 \times {{\,\textrm{GL}\,}}_2\) , and \({{\,\textrm{GSp}\,}}_4 \times {{\,\textrm{GL}\,}}_2 \times {{\,\textrm{GL}\,}}_2\) .