Why would Ben Vereen do all of the following?

Fly a zillion miles to Tunisia for one day to do a few scenes in the "A.D." miniseries.

Risk life and limb -- well, limb anyway -- to be emcee and semi-acrobat for a Ringling Brothers circus special.

Head for Broadway in a play called "Grind" that has already taken its bumps from every critic within 100 miles of Baltimore.

He has the answer:

"Employment," said Vereen. "Call me. My number is . . . Sammy Davis Jr. in his book "Yes I Can" said he tried to be good at everything. I feel that way too. If the door's open, I'll be there. If it's closed, I'll be knocking on it."

This week he's knocking it down. You'll have to be sure not to step out to the refrigerator or you'll miss his part in NBC's "A.D." "I play the Ethiopian who picks up Peter on his way to Samaria," said Vereen. But why spend nearly a day in the air to get to Tunisia for a single day's shooting? "The epic itself attracted me," said Vereen. "I wanted to be on that roster of actors. Also, I had never been to Tunisia. I got to see another country and meet another people."

So just call Ben. Like Mikey, who'll eat anything, Vereen will go anywhere. Like China.

"One day someone called me and asked if I wanted to go bicycling through China," he recalled. "I said sure. We cycled there for three weeks."

That was for a special that never aired, but Vereen still remembers the crowds that turned out to see this unusual black man roll through their countryside. "I was a nice attraction," he said, "not someone they thought was coming to take their jobs."

But the part of the Ethiopian involved a bit more than buying a plane ticket and being fitted for a tunic.

"I went to UCLA's linguistics department and spoke with students from Ethiopia," he said. "I had them record my lines for me so I could listen to the recording and get an Ethiopian accent on my English."

So call Ben. He'll do whatever has to be done to prepare for a part. Like when they called him and asked if he would host a circus special April 15 on CBS. They knew he'd say yes.

"I really didn't get to circuses until I had children of my own," said Vereen. "Now I go all the time." Married and the father of five children, ages 7 to 20, you bet he goes all the time. "I get involved in the acts. I get to hang out with an elephant. I didn't do any high-wire act. This isn't 'Circus of the Stars' where you have four months to rehearse a routine."

But he did try to jump into the middle of an act staged by the Constantines, billed as the only group that does a five- man-high teeter-board act. Vereen tried being the fourth man, poised to catch a member of the troop who was catalted into the air, with the idea of landing on Vereen's shoulders. Vereen missed the catch. Hurt his shoulder too. "Maybe they'll show that," he said, sounding as though he looked forward to seeing his own downfall.

Another sort of downfall may be awaiting him in New York. Vereen, who is one of America's pre-eminent singer- dancer-actors, is scheduled to open on Broadway April 11 in "Grind," a Hal Prince-musical tale of a love triangle between a black top-banana (Vereen), a black stripper and a white Irishman, set against a burlesque house backdrop. The show was not well-received when it played in Baltimore. But then, if the show was perfect to start with, it wouldn't have opened in Baltimore.

"We're doing a lot of things to the show," said Vereen during a pause in rehearsals for previews in New York. "We're sharpening a lot of things. We're doctoring the show. By the time we left Baltimore it was a different show from the one that opened there."

And it will be even more different by the time ew Yorkers see it. "We'll try to clean up the show and get closer to the love triangle," he said. "We're changing some of the dance numbers and songs."

Bob Fosse, a friend of Vereen's since they worked together in "Sweet Charity" and who directed Vereen in Fosse's autobiographical "All That Jazz," sat in the audience one day in Baltimore. "He gave me some points on the character," said Vereen. "He was very helpful."

While he's in New York, Vereen will be with his family in New Jersey and take acting lessons, "sharpening my craft." That craft has won him a mantle of awards, ranging from the Tony to the Drama Desk to to the Theater World to the TV Critics Award for roles like the Leading Player in "Pippin" and Judas in "Jesus Christ Superstar." And there's his most memorable character, Chicken George in "Roots."

TV viewers still remember the character Fiddler in "Roots," played by Lou Gossett, because he was sensitive and strong nd they remember Chicken George because he was colorful, said Vereen. And "Roots" aired eight years ago. "I met a Korean," recalled Vereen, who told him in halting English that he had seen in Korea "a film of a 100- year-old family. He called me Chicken George."

Can it be that Vereen, who didn't go into show business until he was out of high school and who has done so much in so many media for so long a time, is really only 38 years old?

"The things I've accomplished," he says with modesty but with pride, "make it seem like I've been around longer."