  Motivated by the recent discovery of superconductivity in square-planar
nickelates as well as by longstanding puzzling experiments in heavy-fermion
superconductors, we study Cooper pairing between correlated $d$-electrons
coupled to a band of weakly-correlated electrons. We perform self-consistent
large N calculations on an effective $t-J$ model for the $d$-electrons with
additional hybridization. Unlike previous studies of mixed-valent systems, we
focus on parameter regimes where both hybridized bands are relevant to
determining the pairing symmetry. For sufficiently strong hybridization, we
find a robust $s+id$ pairing which breaks time-reversal and point-group
symmetries in the mixed-valent regime. Our results illustrate how intrinsically
multi-band systems such as heavy-fermions can support a number of highly
non-trivial pairing states. They also provide a putative microscopic
realization of previous phenomenological proposals of $s+id$ pairing and
suggest a potential resolution to puzzling experiments in heavy-fermion
superconductors such as U$_{1-x}$Th$_x$Be$_{13}$ which exhibit two
superconducting phase transitions and a full gap at lower temperatures.
