[Nyororin]

Yes, if the visa is a valid work visa.
There is no limit for the maximum amount of work you can do - only the minimum. Once you have the visa you can add jobs, change jobs, etc without any visa problems if you stay above a certain amount of income. (If I recall correctly.)

However, most companies don`t exactly want you working another job on the side that could potentially effect your performance there - and there is the risk of being fired. If you have another full time job lined up, that`s not a big problem. But no, and you risk losing your visa.