The dependence of the strangeness production on the number of nucleons involved in the annihilation process is investigated experimentally in pp and p4 He annihilation at rest. In He, annihilations with the involvement of one and several nucleons (B = 0 and B 1 baryonic number, respectively) are identified. Strangeness enhancement factors, i.e., ratios of K ± , K 0 S , K 0 * and φ meson yields in 4 He to the same yields in H, are derived for final states containing 4 charged mesons (2π + 2π -, π + π -π ∓ K ± , π + π -K + K -). This work completes a previous investigation concerning charged kaon production in meson final states without neutral mesons. The results are compared with our previous ones and with results found in experiments on heavy-ion collisions. It is put in evidence that the strangeness content in the energy blob created by the annihilation has a lower or higher intensity depending on the reaction channel: for instance, π + π -π ∓ K ± production increases with B and π + π -K + K -production decreases. The maximum enhancement factor (about 22) is found for π + π -π -K + without neutral mesons. This value (as well as that concerning π + π + π -K -) is definitely higher than the values predicted by theoretical investigations based on the formation of a highly excited hadronic gas in the annihilation on few nucleons and values found in heavy-ion collisions. Is it the signature of the formation of quark-gluon plasma?