The Washington Redskins will meet their greatest need Thursday when they likely draft Baylor quarterback Robert Griffin III with the No. 2 overall pick. The Heisman Trophy winner is expected to give the Redskins their first elite-level quarterback since the days of Joe Theismann.

But the move isn’t a cure-all for a team that has gone 11-21 in its first two seasons under Coach Mike Shanahan. Despite some important moves in free agency, questions remain elsewhere on the offense.

Look for the Redskins to use their six draft picks in rounds three through seven in the same way they spent 12 selections in the 2011 draft.

Eleven of those 12 rookies earned spots on the 53-man roster at various points last season. (Second-rounder Jarvis Jenkins, who tore his anterior cruciate ligament in the preseason, was the exception.)

Redskins General Manager Bruce Allen said that haul helped cushion the loss of a 2012 second-round pick, which the Redskins traded to St. Louis along with three first-round choices in the Griffin deal. But he and Shanahan intend to continue building through the draft.

That type of mind-set is the mark of a good team, and will ensure a strong foundation and quality depth, said NFL Network draft analyst Mike Mayock.

“To me it’s not just about the first round or the second round or the third round,” Mayock said. “It’s about your volume of picks; how many picks do you have and how many can you hit? . . . Tom Brady is a sixth-round pick. It doesn’t necessarily matter where your all-pros come from, which round, but it just matters that you get enough of them to be good.”

The Redskins used free agency to upgrade Griffin’s supporting cast when they signed wide receivers Pierre Garçon and Josh Morgan. They used the franchise tag to retain the services of top tight end Fred Davis. And the team re-signed center Will Montgomery, who had a solid first season as starter in 2011.

But improving the offensive line still ranks high on the Redskins’ to-do list.

With Jammal Brown rehabbing from a hip injury that has hobbled him in each of the last two seasons, right tackle is a big question. This spring the team re-signed left guard Kory Lichtensteiger, who is working his way back from season-ending knee surgery. He is expected to regain full strength by the time training camp rolls around in July. But a lack of interior line depth crippled the Redskins last season, so the team could pursue a guard-backup center as well.

Options at tackle in the third-round range figure to include Oklahoma’s Donald Stephenson, California’s Mitchell Schwartz, Iowa State’s Kelechi Osemele and Jeff Allen of Illinois.

Stephenson, who visited Redskins Park last month, played with Redskins left tackle Trent Williams at Oklahoma in a zone-blocking scheme similar to Washington’s.

“I think I’d fit real well into their organization,” said Stephenson, who at February’s combine clocked a 4.94-second 40-yard dash — the fastest of any lineman. “At Oklahoma, you have to be able to run to fit into the offense, and it’s the same with the Redskins, them running a similar style. . . . I felt pretty good at my visit.”

Another lineman on the Redskins’ radar seems to be Virginia Tech’s Jaymes Brooks, a mid- to late-round prospect who played guard in the Hokies’ zone-blocking scheme but is believed to have the ability also to play center. Brooks and his agent both have had conversations with the Redskins leading up to the draft.

There’s a strong possibility that Washington will take a tight end in the middle to late rounds of the draft, according to people familiar with the team’s deliberations. Management believes that Davis can rebound from his disappointing end to the season — a four-game suspension for failing multiple drug tests — and continue to build on a breakout campaign.

But a gimpy knee limited fellow tight end Chris Cooley to only five games, and he is owed more than $6 million. He faces an uncertain future with the team. Even as Washington switches second-year pro Niles Paul from receiver to tight end, the team could be interested in Clemson’s Dwayne Allen, Louisiana-Lafayette’s Ladarius Green and Georgia’s Orson Charles. All are projected to go in the third or fourth rounds, where the Redskins hold three picks.

It wouldn’t be surprising to see the team draft a running back, either. The Redskins drafted running backs Roy Helu and Evan Royster in the fourth and sixth rounds, respectively, last season. But Washington has yet to re-sign the 2011 opening day starter, Tim Hightower, whose season ended with a torn ACL in Week 6.

The team could seek to add another backfield option in the draft’s middle to late rounds, where Shanahan has a track record of success. Robert Turbin of Utah State, Cincinnati’s Isaiah Pead and Michigan State’s Edwin Baker rank among the top backs expected to be available.