To take on

If you take on something extra, means you are accepting an extra responsibility. If someone is having difficulty doing something, then you take up for them meaning help them.

Example: 

    1- Hey John, Will you be kind enough to take up my shift for tomorrow? I will cover you up whenever you need me to.

2- My worst mistake ever in this building was when I agreed to take up extra work hoping to be paid more than usual.