**Question:** What is the finest topology on $\mathrm{CAlg}$ (commutative ring spectra) for which *THH* (Topological Hochschild Homology) satisfies descent?

Adaptations of the arguments appearing in Section 3 of BMS2 show that *THH* has flat descent for simplicial commutative rings. However, the methods therein cannot be used to check whether *THH* has flat (or any weaker form of) descent for commutative ring spectra; simplicial $R$-algebras have the special property of being the nonabelian derived category of the category of finitely generated polynomial $R$-algebras.