TiNiSn is an intensively studied half-Heusler alloy that shows great potential for waste heat recovery. Here, we report on the structures and thermoelectric properties of a series of metal-rich TiNi1+ySn compositions prepared via solid-state reactions and hot pressing. A general relation between the amount of interstitial Ni and lattice parameter is determined from neutron powder diffraction. High-resolution synchrotron X-ray powder diffraction reveals the occurrence of strain broadening upon hot pressing, which is attributed to the metastable arrangement of interstitial Ni. Hall measurements confirm that interstitial Ni causes weak n-type doping and a reduction in carrier mobility, which limits the power factor to 2.5–3 mW m−1 K−2 for these samples. The thermal conductivity was modelled within the Callaway approximation and is quantitively linked to the amount of interstitial Ni, resulting in a predicted value of 12.7 W m−1 K−1 at 323 K for stoichiometric TiNiSn. Interstitial Ni leads to a reduction of the thermal band gap and moves the peak ZT = 0.4 to lower temperatures, thus offering the possibility to engineer a broad ZT plateau. This work adds further insight into the impact of small amounts of interstitial Ni on the thermal and electrical transport of TiNiSn.