Sure.
I have done that many times. Sometimes I have also had a bear tag too, especially in Idaho.
The only tag I use that for me so far has never been in the same area or a the same time for open seasons are Antelope. When I hunt antelope it's usually only antelope. There are some elk and antelope overlaps, but I have never hunting them both at the same time in the same area. Most times the 2 seasons do not overlap. But depending on the area it's not uncommon to hunt deer bear and elk at the same time.
