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In this work, we expand on the XENON1T nuclear recoil searches to study the individual signals of dark matter interactions from operators up to dimension eight in a chiral effective field theory (ChEFT) and a model of inelastic dark matter (iDM). We analyze data from two science runs of the XENON1T detector totaling $1\mathrm{t}\times \mathrm{yr}$exposure. For these analyses, we extended the region of interest from $[4.9,40.9]{\mathrm{keV}}_{\mathrm{NR}}$to $[4.9,54.4]{\mathrm{keV}}_{\mathrm{NR}}$to enhance our sensitivity for signals that peak at nonzero energies. We show that the data are consistent with the background-only hypothesis, with a small background overfluctuation observed peaking between 20 and $50{\mathrm{keV}}_{\mathrm{NR}}$, resulting in a maximum local discovery significance of $1.7\sigma$for the $\mathrm{Vector}\otimes {\text{Vector}}_{\text{strange}}$ChEFT channel for a dark matter particle of $70\mathrm{GeV}/c^2$and $1.8\sigma$for an iDM particle of $50\mathrm{GeV}/c^2$with a mass splitting of $100\mathrm{keV}/c^2$. For each model, we report 90% confidence level upper limits. We also report upper limits on three benchmark models of dark matter interaction using ChEFT where we investigate the effect of isospin-breaking interactions. We observe rate-driven cancellations in regions of the isospin-breaking couplings, leading to up to 6 orders of magnitude weaker upper limits with respect to the isospin-conserving case. Published by the American Physical Society2024