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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.