"Rung 3.5" exchange-correlation functionals for Kohn-Sham density functional theory depend linearly on the nonlocal one-particle density matrix of the noninteracting Kohn-Sham reference system. Rung 3.5 functionals also require a semilocal model for the one-particle density matrix. This work presents new model density matrices for Rung 3.5 functionals. The resulting functionals give reasonable predictions for total energies, molecular thermochemistry and kinetics, odd-electron bonds, and conjugated polymer bandgaps. Global-hybrid-like combinations of semilocal and Rung 3.5 exchange, and empirical density matrix models, also show promise.