Can a check box or radio button allow multiple selections in required field(s)?.

The initial selection would be required, however the ability to also select other choices in addition to the original selection. In my attempt to setup, I can select one field (required) but selecting an additional field "unchecked" the original field selected

Something like:

Reason(s) for cancelling

Option 1

Option 2

Option 3

Option 4

In the use case, both Option 1 and Option 3 could be selected.