Welcome to the community, Apryl!
What you want is possible, but a little more information can help with the details.
Do you want something like a chore chart?
How does your schedule rotate?
Do you want a calendar view that lists the employee for each day? How far do you want the calendar to stretch out?
Do you want to store historic information, such as the result of the task? Or are you only concerned about the current week/month and don’t need historic or future data?
Does the task already exist in a base? Are there multiple tasks?