"Shake hands with" is a common expression used to describe the action of grasping someone's hand and moving it up and down. However, there are other phrases that could be used as synonyms for this gesture. For example, you could say, "greet with a handshake," "exchange handshakes," "shake hands cordially," "trade firm handshakes," "clasp hands in friendship," or simply "shake hands." Each of these phrases highlights the act of greeting or establishing a connection with another person through an exchange of handshakes. No matter which phrase you choose, the important thing is to make a positive first impression and show that you are friendly and open to new connections.