Does it mean;
*** My plate is already full. ***

I already have lots of food in my plate. and I have a lot of work already.

Question

Does it mean;
*** My plate is already full.  ***

I already have lots of food in my plate.    and   I have a lot of work already.

Answer

When you say my plate is full is has nothing to do with food.   It is talking about your schedule meaning I am so busy I cannot take on another job.   Its an idiom.