1. An expression used to reinforce an argument or statement by indicating that a conclusion applies even more strongly to a particular case than to a previous one
If John succeeded without training, then with greater reason, Mary should succeed since she has extensive training.
Se João conseguiu sem treinamento, com maior razão Maria deveria conseguir já que tem treinamento extenso.
2. Used to emphasize that something is even more applicable or valid in a given context
He was rejected for the position; with all the more reason, his less qualified brother shouldn't apply.
Ele foi rejeitado para o cargo; com maior razão, seu irmão menos qualificado não deveria se candidatar.