The non-magnetic heavy fermion compound Ce3Co4Sn13 was studied under pressure. We report single crystalline measurements of electrical resistivity as a function of temperature ρ(T) under pressure. Some characteristic features related to a structural transition (TS), crystalline field effects (TCEF), and a low temperature maximum (Tmax), possibly connected simultaneously to the onset of Kondo lattice coherence and short range magnetic correlations, were identified in the ρ(T) data. A pressure-temperature phase diagram with TS and Tmax was constructed by mapping these features. Like for most Ce-based heavy fermion compounds, Tmax moves to higher temperatures with pressure, indicating that it is related to the Kondo energy scale, due to the increase of hybridization induced by pressure. On the other hand, TS, associated to a superlattice distortion and probably combined with a charge density wave transition, decreases as a function of pressure. However, differently from the Sr3−xCaxIr4Sn13 system, where a superlattice quantum phase transition is observed [L. E. Klintberg et al., Phys. Rev. Lett. 109, 237 008 (2012)], in Ce3Co4Sn13 TS ∼ 154 K, at ambient pressure (P = 0), seems to stabilize at around 143 K for P ≥ 19 kilobars. We also investigated ρ(T) in external magnetic fields, at P = 0. Negative magnetoresistance and increase of Tmax are observed, suggesting suppression of low temperature short range magnetic correlations.