You don’t have to pass the counter as an argument to the event function, you can define the count variable as a global variable (persistent) and increment/decrement it, while not terminating the integration, until the control arrives at a count to terminate the integration.
The following snippet can be used as an example, for 10 events.
function [value,isterminal,direction] = Eventsfcn(t,y)
count = 10;
if count > 1
count = count - 1;
isterminal = 0;
isterminal = 1;