  We explore computationally tractable deformations of the SYK model. The
deformed theories are described by the sum of two SYK Hamiltonians with
differing numbers, $q$ and $\tilde{q}$, of interacting fermions. In the large
$N$ limit, employing analytic and numerical tools, we compute finite
temperature correlation functions and thermodynamic quantities. We identify a
novel analytically solvable model in the large $q$ limit. We find that, under
certain circumstances, the thermal RG flow in the strongly coupled infrared
phase exhibits two regions of linear-in-temperature entropy, which we interpret
in terms of Schwarzian actions. Using conformal perturbation theory we compute
the leading relevant correction away from the intermediate near-conformal fixed
point. Holographic spacetimes in two spacetime dimensions that reproduce the
thermodynamics of the microphysical theory are discussed. These are flow
geometries that interpolate between two Euclidean near-AdS$_2$ spacetimes with
different radii. The Schwarzian soft mode corresponding to the AdS$_2$ region
in the deep interior resides entirely within the geometric regime.
