The Saints Ring of Honor grows by one at halftime Monday when kicker Morten Andersen becomes the fourth person whose name is displayed on the terrace level fascia of the Mercedes-Benz Superdome.

Archie Manning, Rickey Jackson and Willie Roaf made up inaugural group whose names were unveiled in 2013.

Chances are, they’ll never get all the way around before a new stadium takes the Dome’s place decades from now.

Which is the way it’s intended.

Unlike the Saints Hall of Fame, also located in the Superdome, which has 47 members, this one is meant to be exclusive.

“We wanted to make this one very tough to get into,” Saints coach Sean Payton said when Andersen’s election was announced in August. “It might be three years before we have another.”

Unlike the banners that hung in the Superdome until 2013, the Saints have control over the selection thanks to the 2009 deal that gives the team all fixed signage decisions, and thus the ring is limited to those associated with the Saints.

There were three non-Saints with banners, Dave Dixon, Pete Maravich and Eddie Robinson. Dixon has one of the streets around the Dome named for him, Maravich has a banner in the Smoothie King Center, and team spokesman Greg Bensel said a way to properly honor Robinson is being considered.

The selection is done by a committee of ownership, front office members, former players and select media members.

The only stated eligibility criteria is that an inductee must be a former player, administrator or other individual who has played a significant role both on and off the field in the franchise’s history.

That’s pretty much in line with other teams’ criteria, which the Saints studied before establishing their own.

Dallas had the first, beginning in 1975 when the Cowboys inducted Bob Lilly. That number’s now up to 21.

In Baltimore, where both the Ravens and Baltimore Colts are included, it’s 17.

There are no pre-Indianapolis Colts in the RCA Dome, but Jim Harbaugh, who played there for only four seasons is one of 11 who made it.

In Green Bay, you have to be in the Pro Football Hall of Fame. But with 22 ex-Packers in Canton, Ohio, and more on the way, there’s no shortage.

The Atlanta Falcons, which came into existence a year before the Saints, have nine in their ring, which debuted in 2004.

Not that copying the Dirty Birds is always advisable, but that seems like a pretty good pace to follow.

But who should be next in line for the Saints?

The first four have set the high standard the team has declared the ring.

Roaf and Jackson are in Canton. Manning isn’t, but his contributions during the franchise’s trying period speak for themselves.

Certainly playing in more games and scoring more points than anyone in NFL history more than qualifies Andersen, who spent 13 of his 25 seasons with the Saints.

Current players like Drew Brees, Marques Colston and Jahri Evans plus Payton look to be in the ring someday, but they’re not yet eligible.

Until those days come, here then, should be the next five:

1. Jim Finks

The only person associated with the Saints other than Jackson and Roaf to be given a Pro Football Hall of Fame biography in the team’s media guide, the president and general manager of the team from 1986 until 1993 when cancer forced his retirement and ultimately cost him his life a year later, Finks was the architect of the franchise’s emergence from two decades of at-best mediocrity to its first playoff berth in 1987.

After Finks’ retirement, the Saints never again made the playoffs under Jim Mora.

2. Deuce McAllister

McAllister is the team’s career rushing yardage (6,096) and rushing touchdowns (49) leader, despite having to share time with Rickey Williams early and Reggie Bush later and dealing with injuries that unfortunately ended his playing days a year before the Saints’ Super Bowl season.

And yet, he was so highly thought of that the team brought him back before the playoffs making him an honorary captain and having him lead the team on the field for the divisional round game against Arizona.

3. Sam Mills

The heart and soul of the Dome Patrol, the former USFL player out of Montclair State made four Pro Bowls during his tenure with the Saints (1986-94).

Mora calls him, “The best player I ever coached.”

Free agency took him to Carolina, where he played for only three more seasons but was so revered that he not only is in the Panthers’ Ring of Honor but merited a statue.

All of football mourned Mills’ death due to cancer in 2005 at age 46.

4. Dalton Hilliard

Before Bush, the Saints never had a more versatile back.

The former LSU star from Patterson is third in career rushing yards (4,164) and second in rushing touchdowns (39). He also has 2,223 receiving yards and 14 touchdowns.

Hilliard also had the distinction of completing four passes — all of which went for touchdowns.

5. Bobby Herbert

Does anyone else represent the ups and downs of the franchise better than the Cajun Cannon?

He quarterbacked the Saints to their first playoff appearance, sat out a season in a contract dispute that helped lead to free agency, and returned for two more seasons and two more playoffs appearances before finishing up his career in Atlanta, much to the chagrin of the Who Dats.

And now, he’s parlayed that into a broadcasting career in which he created Who Dat Nation and has become the voice of the fan in good and bad.