The Dolphins of the early 80's did just that. David Woodley was the starter, but he was inconsistent, so Don Strock would relieve him. It happened so often that it became a two QB system known as Woodstrock.Â
When they got shut down in the '82 Super Bowl, Shula broke it up. Sent Woodley packing, made Strock strictly a backup QB, and drafted Dan the Man.
Actually, you have that a little out of text. It is true the Dolphins used 2 Qb's in the 1982 SB season, nicknamed "Woodstrock". At the start of the '83 season, Don Shula said he had to start David Woodley because he just helped lead us to the Super Bowl. His play was inconsistent and the Dolphins stood at 3-2 after 5 games. Shula started Marino in the 6th game & he went 7-2 as a starter. The Dolphins stood at 10-4 after 14 games. Marino hurt his knee @ Houston and Don Strock started the last 2 games of the season, winning both. The Dolphins went 12-4 on the season winning the division in effect using 3 different Qb's!!! Woodley, Strock, & Marino were for that 1 season all on the same team together.
Woodley was later sent to Pittsburgh where he & Marino faced off in 1984 @ Pittsburgh, with the Dolphins winning that game & Marino probably thinking..... I took your job!!! The way you have it stated is that Woodley never was a part of the '83 team, & they drafted Marino straight in as starter, with Strock as his backup & that's not correct. The above scenario is relatively correct. I don't remember exactly when Woodley was dumped, but, you have to figure he was there at least half of the '83 season because he did start 5 full games & that's almost half the season.