Disordered photonic materials can diffuse and localize light through random multiple scattering, offering opportunities to study mesoscopic phenomena, control light-matter interactions, and provide new strategies for photonic applications. Light transport in such media is governed by photonic modes characterized by resonances with finite spectral width and spatial extent. Considerable steps have been made recently towards control over the transport using wavefront shaping techniques. The selective engineering of individual modes, however, has been addressed only theoretically. Here, we experimentally demonstrate the possibility to engineer the confinement and the mutual interaction of modes in a two-dimensional disordered photonic structure. The strong light confinement is achieved at the fabrication stage by an optimization of the structure, and an accurate and local tuning of the mode resonance frequencies is achieved via post-fabrication processes. To show the versatility of our technique, we selectively control the detuning between overlapping localized modes and observe both frequency crossing and anti-crossing behaviours, thereby paving the way for the creation of open transmission channels in strongly scattering media.