Taylor Miles and Elliot Omozusi became the latest two players to agree new deals for next season.
Miles, who joined the Clarets in January, made 15 appearances for Rod Stringer’s side last season, scoring one goal in the process.
Omozusi also netted once, but turned out for the Clarets on 46 occasions, both at centre back and right back over the course of the season.
They join Church, Giles and Porter on this year’s “retained” list.
Meanwhile, goalkeeper Sam Beasant has followed in the footsteps of Danny Green and signed for Concord Rangers. The former Cambridge United stopper made 45 appearances for the Clarets last season, but drifted out of favour towards the end of the campaign, with Jake Jessup replacing him.