If you're regularly getting re-appointed to games (assume you mean that you get a league game, then get a county appointment from the FA which trumps it?) then you need to speak to your CFA about how they manage closed dates.
Once I get allocated a league fixture then I'll close the date with the FA so that they don't come to me with a late switch that I have to turn down (and upset the FA) or take (and upset my league). The county games are usually allocated far enough in advance that I'll know if I have one before I get my league allocation, and it just prevents that awkward situation.
It depends on the game youve been appointed to by your CFA, but if you turn down a county cup appointnent then you cant referee a sunday league game on the same day.
1 - The FA cup
2 - The Premier League
3 - The Football League
4 - The FA Trophy
5 - The FA Vase
6 - County Cup Competitions (nominated senior competition only, or semi- final or final in any other competition)
7 - The Panel Leagues
8 - The FA Youth, FA County Youth, FA Womens Cup (4th round and above)
9 - Contrib Leagues (recognised divisions only), Nation League Systems Cup and FA Sunday Cup
10 - FA Womens Super League and Cup
11 - Supply Leagues (marking divisions only)
12 - FA Womens Premier League and Cup
13 - Senior County Leagues
14 - Intermediate County Leagues
15 - FA womens cup prior to 4th round
16 - Womens Combination League and Cup
17 - Womens Regional League and Cup
18 - County Junior Leagues
19 - County Womens League and Cup
20 - All other competitions
So, for those of us who are at the bottom of the pile, if we close a date with the county then we shouldnt be refereeing any other games.
While you could do a botom division sunday league game, i think your CFA would take a dim view of it if they found out.