In several experimental systems phase diagrams coverage-temperature show a strong asymmetry. This behavior can be reproduced by including non-additive lateral interactions. In this work a Monte Carlo study on the canonical assembly of the criticality of monomer adsorption with non-additive interactions is presented. Traditional pairwise energies were replaced by other more general ones where the lateral interaction between two ad-atoms depends on the coverage at first sphere of coordination. This kind of energies includes multibody interactions like three-body interactions and four-body interactions, etc. These energies induce the formation of several non-additive ordered structures. Finite size scaling method was used to classify the order of phase transition of each non-additive phase. On the other hand, the corresponding phase diagrams are formed naturally, in which case the diagrams show strong asymmetries.