You looking for an action match or precision? I know palo alto does a precision match, not sure of the dates. There are several matches around that do outlaw steel and steel challenge. Every now and then there are some USPSA style rifle matches that include rimfire. There was a match this weekend in Hattisburg that had 8 USPSA style stages and you could use a rimfire rifle, but the match has been cancelled. There is a match Sunday at tangi that is a hybrid steel outlaw match.
Fusilier Complex has the Whirling 22s this Sunday. It’s rife and pistol, each used for each of the 6 or so stages. Timed par time stages, mostly steel, but different props.
They also started shooting steel silhouette there as well. That’s the last Saturday of each month. If you go to their website, these matches are listed on the events/calendar.
They also plan to do a PRS style match in the spring.