Infielder Jurickson Profar falls into that category. Also filing were pitchers Shawn Tolleson, Jake Diekman, Tanner Scheppers and Tom Wilhelmsen, first baseman Mitch Moreland and catcher Robinson Chirinos.
On Wednesday, Wilhelmsen agreed to a one-year contract for 2016.
"It means something to me, yeah," Tolleson said. "It means my salary [could] be decided for me."
Tolleson is in his first year of arbitration, so he is due for a significant raise after saving 35 games for the Rangers in 2015. He made approximately $520,000 in 2015.
Chirinos, Diekman and Scheppers are also in their first year of arbitration. This will be the last year for Moreland, who can be a free agent after this season. He filed at $3.25 million last winter with the club offering $2.025 million. He eventually settled at $2.95 million without a hearing.
Wilhelmsen went to an arbitration hearing with the Mariners last season and lost. He made $1.4 million after filing for $2.2 million. The Rangers avoided an arbitration hearing with catcher Chris Gimenez earlier in the offseason when he agreed to a $975,000 contract for 2016. Pitcher Nick Tepesch also was eligible but was non-tendered by the club.
The Rangers have not had a player go to arbitration since Lee Stevens in 2000. The Rangers are not a file-and-trial club. There are some clubs that stop negotiating with their players once the numbers are exchanged, but the Rangers have not adopted that philosophy.
The Rangers came close to a hearing with Mike Napoli in 2012 before reaching a settlement right up against the deadline.
T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields, follow him on Twitter @Sullivan_Ranger and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.