The phrase "to go on with" means to continue or proceed with something, despite any obstacles or difficulties that may arise. It implies determination and perseverance in pursuing a goal or objective, even when faced with challenges or setbacks.
There's always something going on with others that we'll never truly understand. (creativeboom.com)
If you want to find out what's really going on with someone of the opposite sex, read his or her body language. (questchat.com)
And then we always have lots going on with holiday parties and events and classroom things, so getting the decor up and finished feels great! (honeywerehome.com)