Reprogrammable integrated optics provides a natural platform for tunable quantum photonic circuits, but faces challenges when high dimensions and high connectivity are involved. Here, we implement high-dimensional linear transformations on spatial modes of photons using wavefront shaping together with mode mixing in a multimode fiber, and measure photon correlations using a time-tagging single-photon avalanche diode (SPAD) array. Our demonstration of a generalization of a Hong-Ou-Mandel interference to 22 output ports shows the scalability potential of wavefront shaping in complex media in conjunction with SPAD arrays for implementing highwe achieved (80.5 +/- 6.8)% similarity for indistinguishable photon pairs and (84.9 +/- 7.0)% similarity for distinguishable photon pairs using 22 detectors and random circuits.