I'm not sure what you mean by "close calendar periods", but you can only have one Time Profile per Cube. A Time Profile includes a number of years, of course.
This said, different Scenarios can work with different levels of such profile, i.e. one can have weekly data and the other can have monthly data, so typically you can still accommodate all data in one cube if you wish. The setting can even change by time, so you can have scenarios that start as weekly and become monthly later on, or viceversa.
If that's not enough, you can still display data from other cubes through a Dynamic Calc formula on a member (typically a UD8), which runs at reporting time and can retrieve data from anywhere.