We aim to present a comprehensive theoretical investigation of dielectronic recombination (DR) of the silicon-like isoelectronic sequence and provide DR and radiative recombination (RR) data that can be used within a generalized collisional-radiative modelling framework. Total and final-state level-resolved DR and RR rate coefficients for the ground and metastable initial levels of 16 ions between $rm{P^{+}}$ and $rm{Zn^{16+}}$ are determined. We carried out multi-configurational Breit-Pauli (MCBP) DR calculations for silicon-like ions in the independent processes, isolated resonance, distorted wave (IPIRDW) approximation. Both $Delta n_c =0$ and $Delta n_c =1$ core excitations are included using $LS$ and intermediate coupling schemes. Results are presented for a selected number of ions and compared to all other existing theoretical and experimental data. The total dielectronic and radiative recombination rate coefficients for the ground state are presented in tabulated form for easy implementation into spectral modelling codes. These data can also be accessed from the Atomic Data and Analysis Structure (ADAS) OPEN-ADAS database. This work is a part of an assembly of a dielectronic recombination database for the modelling of dynamic finite-density plasmas.