Forest Green Rovers chairman Dale Vince wants more than two promotion places between the National League and League Two, calling for a “proper exchange of clubs” between the two divisions.
Two teams go up from the fifth tier each season, with one automatic spot.
“There is a good reason for there being four up and four down between Leagues Two and One. That should extend to the National League,” Vince told BBC Sport.
“There is a kind of glass ceiling between our league and League Two.”
Vince’s Gloucestershire club are third in the National League with 15 games remaining, four points below leaders Lincoln City.
They lost to Grimsby in last season’s play-off final at Wembley after finishing second, and were fifth in 2014-15.
While two National League sides – Lincoln and Sutton United – have reached the FA Cup fifth round, there are no League Two sides in the last 16.
In-form Lincoln, who have beaten Championship sides Brighton and Ipswich in the past two rounds, travel to top-flight Burnley on Saturday, while Sutton, who are 17th in the National League, host Arsenal on Monday.
‘Give more clubs chance to progress’
“There are some very strong, capable teams in the National League,” Vince added. “They are kept in this league, restricted by the promotion opportunities.
“The FA have this curious way of defining everything below League Two as ‘non-league’ football.
“A proper opportunity for an exchange of clubs between the National League and League Two would be better for the game and give clubs more chance to progress, those that are moving in the right direction.”
Play-offs were introduced to the National League in 2002, prior to which only one team was relegated and promoted each season between tiers four and five.
Speaking in 2013, then-Cambridge United boss Richard Money described the promotion system in place in the National League as “outdated” and “nonsense”.