${\mathrm{Fe}}_{2}\mathrm{P}$-based magnets are known for their significant magnetic properties, making them useful in various technological applications. The aim of this study was to investigate the effects of Si and Co substitution on the physical and magnetic properties of the ${\mathrm{Fe}}_{2}\mathrm{P}$ compounds. In order to have a systematic understanding we have performed combined ab initio calculations and a set of experiments. Particular emphasis was placed on the study of preferential substitution sites, lattice constants, magnetic moments, and the Curie temperature (${T}_{C}$), which was further explored by considering the exchange interaction energies ${J}_{ij}$. Satisfactory agreement was observed between theoretical calculations and the predicted phase transition from the hexagonal to the body-centered-orthorhombic (BCO) crystal structure as a function of temperature. Theoretical calculations reveal that the $2c$ position is the preferred site for Si, while Co is expected to occupy the $3f$ sites. Theoretical analysis of the magnetic moments shows an increase up to $3.64\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{B}/\mathrm{f}.\mathrm{u}.$ for $x$ = 0.5 Si, which agrees with the experimental values of $3.16\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{B}/\mathrm{f}.\mathrm{u}.$ Co substitution in ${\mathrm{Fe}}_{2\ensuremath{-}y}{\mathrm{Co}}_{y}{\mathrm{P}}_{0.84}{\mathrm{Si}}_{0.16}$ and ${\mathrm{Fe}}_{2\ensuremath{-}y}{\mathrm{Co}}_{y}{\mathrm{P}}_{0.59}{\mathrm{Si}}_{0.41}$ resulted in a decrease in magnetic moments and consequently in other magnetic properties. Focusing on the Curie temperature, three different trends were found depending on the Si concentration. A dependence of the $3f\text{\ensuremath{-}}3f$ intralayer exchange interaction energies on Si was proposed as the reason for the trends and deduced as the reason for an increase in ${T}_{C}$ at low, no change in ${T}_{C}$ at medium, and a decrease in ${T}_{C}$ at high Si concentrations.