The last-placed Tigers currently have 18 players on their injury list, leaving them in a battle just to field a team every week.
The 10th-placed Bulldogs (5-5) have also been hit hard this year with 10 players currently in their injury ward, including stars such as Sam Darcy (ACL), Tim English (concussion), Tom Liberatore (concussion/knee), Cody Weightman (knee) and Bailey Williams (hamstring).
Beveridge is hopeful James O'Donnell (hamstring) will return for Sunday's clash with in-form Melbourne (7-3) at Marvel Stadium, while Weightman and English could be one to two weeks away.
But with the physical toll on players seemingly at an all-time high, Beveridge hopes the AFL will soon act to allow clubs to increase list sizes and have more flexible player promotion rules.
"One of the things, talking about having conversations with the AFL, I think we need more fluidity in the scope to bring players on to an AFL list to be able to play them," Beveridge told reporters on Thursday.
"Richmond are probably now a primary example, where you'd like a supplementary list to be able to feed players into it to call on them as your injury toll worsens.
"I mean, the 23 rounds, the pre-season games are still there, with Tasmania coming in there's likely to be another round.
"With only 42 (players) outside of category B, it's not enough on a list, I don't think.
"I think the opportunity to have a four to six supplementary approach and maybe even send it out a bit further for a team and club like Richmond who are really feeling the pinch with their injury toll (is important), so you can bring players up and play them as the year goes on."
Tasmania, who enter the AFL in 2028, will be allowed up to 48 players on their list for their first few years.
Beveridge says other clubs should also be given that capability, but concedes there are still details that would need to be worked through.
"There's a bit to work through around the detail of that and who comes off (the list) and what hold you've got on them at the end of the year, but I really feel like we need that," Beveridge said.
"It's something for the future,
"I think Tasmania ... the plans for their list building and how many they'll have on their list, I think every AFL club should have the scope to have something similar if you've got an injury toll like some of the clubs have."
