There are several synonyms for the phrase "put the pressure on". One common alternative is "apply pressure", which carries a similar meaning of exerting force or influence in order to achieve a desired outcome. "Put the squeeze on" is a more informal option that implies a stronger and more forceful approach. Other synonyms include "push", "encourage", and "motivate". Ultimately, the choice of synonym will depend on the specific context and tone of the situation at hand. Whether in business negotiations or personal relationships, using the right words to convey your intentions is key to successfully achieving your goals.