To continue.
carry on
To activate something.
turn on
To do something repeatedly.
keep on
To give a lot of attention to one particular person, subject or thing.
focus on
To connect to a computer system by typing your name, so that you can start working.
log on
To land on something after raising yourself in the air.
jump on
To accept a particular job or resposibility.
take on
To need a particular thing or the help and support of someone or something in order to continue to work correctly or to succeed.
rely on
To create a story, the events of which come from a previous piece of work.
base on
To continue a concert or sports event after the time it is supposed to finish.
play on