How to use a “case” statement inside a select statement in Bash script?

I’m fairly certain the *) option in the case statement never executes if the case statement is embedded inside a select statement.

PS3=$'nEnter one above: '
count=0
select rb in "varone" "vartwo" "Exit"; do 
[[ $count -ge 3 ]] && break
    case $rb in
        varone)
          echo "bingo";;
        vartwo)
          echo "bango";;
        Exit)
          break;;
        *)
          ((count++))
    esac
done

That being said, is there any way to accomplish what my code is attempting i.e. just keep a count of empty responses and exit if like in my example 3 such responses?