As he and his relatives feud over who will inherit his sports franchises when he dies, Saints and Pelicans owner Tom Benson said in a new legal filing Tuesday that he is willing to meet with an Orleans Parish Civil District Court judge privately in an effort to prove it is not necessary for him to undergo a mental examination.

Meanwhile, in a separate civil court filing, the relatives Benson wants to cut out of a succession plan involving the Saints, Pelicans and other businesses defended themselves against his claim that he reached such a drastic decision only after years of worrying about their professional competence.

If that were true, they said, then Benson would not have successfully sought reaffirmation from the NFL last year for a plan for him to leave — upon his death — all voting shares of the Saints to his daughter, Renee Benson; his granddaughter, Rita LeBlanc; and his grandson, Ryan LeBlanc, with long-time team executive Rita as the franchise’s representative to the league.

For his part, Benson argued through his lawyers that if he is ultimately ordered to submit to a psychiatric evaluation, it should be conducted by an independent physician who was not suggested by the attorneys for Renee, Rita and Ryan.

Renee, Rita and Ryan alleged in court documents filed previously that it is “clearly” necessary for the 87-year-old billionaire to be examined by a geriatric psychiatrist because his physical and mental state is in dispute.

They alleged he exhibited “a pattern of bizarre behavior” before the two-time widower decided in January that he wanted his third wife — Gayle, whom he married in 2004 — to inherit his billion-dollar business empire upon his death. Benson’s relatives requested that psychiatrist Dr. Ted Bloch III be allowed to examine the octogenarian in a confidential setting.

But Benson filed documents Tuesday saying he reserved the right if necessary to challenge the expert credentials of Bloch, experienced though he may be. Bloch graduated from LSU medical school in 1989. He has been certified with the American Board of Psychiatry and Neurology in geriatric psychiatry since 1995, and he was recertified in August 2008, according to court documents.

Benson also reiterated his position that his relatives do not have a legal basis to have his mental state examined, accusing them of doing little more than mentioning his advanced age and providing anecdotes of the supposed deterioration of his health in their filings.

“They have alleged only isolated, discrete events and conditions from which Mr. Benson has recovered,” Tuesday’s filing on behalf of the Saints and Pelicans owner read.

Benson — as well as his lawyers Phillip Wittmann, James Gulotta and Matthew Almon — contended the relatives wanted “to go on a fishing expedition” for material they could use against him with the medical evaluation they were seeking.

In documents defending their position Tuesday, Renee, Rita and Ryan — represented by attorneys Randy Smith and Stephen Gelé — counter that what they cite in their motion to have Benson checked out by a psychiatrist is enough under modern Louisiana law to justify such a proceeding.

As evidence that Benson has not been acting rationally, they cite his attempt to purchase the Fair Grounds Race Course and Slots in New Orleans despite having been the chairman of the NFL Finance Committee that established rules prohibiting league owners from acquiring gambling interests.

They also claim he has failed to fulfill basic duties as the trustee of a trust set up in Texas by his first wife, Shirley, who died of lupus in 1980, that includes her daughter Renee and grandchildren Rita and Ryan among the beneficiaries. According to the three ousted heirs, the duties Benson has neglected include paying insurance premiums, property taxes, rent on an aircraft hangar and the monthly management fee for a company owned by Renee that oversees and coordinates multiple car dealerships.

A judge in San Antonio — into which Benson’s business empire extends — signed a restraining order in January that among other things temporarily froze the assets associated with the trust. A hearing on that matter is scheduled for Wednesday in San Antonio.

Furthermore, to refute statements he’s made about their alleged incompetence, Benson’s relatives in their filing document the roles they’ve held for years in his various businesses: Rita with the sports franchises; Ryan with the car dealerships and the family ranch near San Antonio; and Renee with all of those and some banks as well.

Benson didn’t seem displeased with them when he had his original succession plan re-ratified last year, Rita, Ryan and Renee said in court.

They said it was irrational that they were fired from any participation in Benson’s business empire shortly after a letter signed by him was sent to them on Dec. 27 saying they were no longer welcome to contact him.

“Tom Benson is no longer in a position to care for himself and needs this court’s assistance to protect him,” Rita, Renee and Ryan’s filing Tuesday said. A Feb. 10 hearing has been set before Civil District Judge Kern Reese.

Starting his career as a bookkeeper and manager at a Chevrolet dealership in his hometown of New Orleans in 1948, Benson eventually became Louisiana’s sole billionaire thanks largely to his purchase of the NFL’s Saints in 1985 and the NBA’s Pelicans — then known as the Hornets — in 2012. On Jan. 21, he revealed he wanted Gayle Benson to take over for him when he dies.

Ryan, Renee and Rita quickly launched a legal challenge to Benson’s new plans, filing a civil suit that alleged the family patriarch was being unduly influenced while in a weakened mental and physical state. They also alleged that he was improperly attempting to wrest away assets he had folded into trusts he had set up for their benefit.

Last Tuesday, Benson’s lawyers — in a court filing contesting the relatives’ claims about his mental state — said Renee, Rita and Ryan had never managed to convince him of their competence to run his businesses, even after years of being groomed to one day assume the reins.

That, they said, is mainly why Benson decided to make his wife his principal heir, though he also didn’t like the way his relatives had treated Gayle after she married him.

Benson’s legal filings have taken care to point out that Rita, Ryan and Renee “are still beneficiaries of various trust interests that Mr. Benson has established for them, and they will continue to enjoy the hundreds of millions of dollars they have been given.”