Just to clarify your terminology, you can only have one primary key per table, although it can be composed of several columns.
There is nothing wrong with this sort of arrangement, and it is quite common when recording histories, for example, if you wanted to record the number of units produced by each factory worker on a production line you might have a table with these columns:
WorkerID
Date
UnitType
UnitsProduced
Note: the worker may work on several different types of units during a single day.
The primary key would encompass the first three columns, as these are expected to be unique.