I read somewhere that if you loan him to the Marlies for a conditioning stint he starts counting on the cap at that point. I think it was an article in the Athletic.
That would likely squash that possibility but I do think they will get him into a game or 2 in games 55/56 which will essentially be meaningless games as far as the standings go anyway.
This was prior to the Sandin callup, so the numbers are all off by 0.894167m; Sandin too would have to be sent down

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Mirtle: Are the Maple Leafs engaging in 'LTIR shenanigans' with Frederik Andersen?
Leafs have (roughly) 1.3m cap space & would need to clear (roughly) 3.7m to bring in Andersen to the Leafs
or Marlies (even on a conditioning stint he counts against the cap). There's a problem though,
"any players who are on an NHL roster on deadline day are not eligible to be sent down to the minors or taxi squad", they however can send down Sabourin & Robertson which frees up 1.521667m cap space.
So the Leafs would still have about another
2.178333m to clear (I think it's slightly less than that but not by a whole lot), so if they want to bring back Andersen they have
2 options:
1) Add players to LTIR
2) Trade (
"While the deadline has passed, this is technically allowed, although none of the players who are dealt would be allowed to play for their new organization until next season")
Bogo's 1m is on LTIR, so that number is now roughly
1.178333m; Hyman is out but only for 2+ weeks, his timeline of arrival is likely way too early to have him placed on LTIR for the remainder of the regular season unless: a) that expected injury timeline changes; or b) the Leafs do some sneaky business, unlikely.
Mirtle suggested the possibility of trading Kerfoot to Seattle which would really suck for the Leafs' playoff run. The good thing is it doesn't look like that would be necessary, it looks as though trading
Engvall & his 1.25m cap hit would be the likely answer; would suck to lose him but Engvall is likely the lowest cost of bringing back Andersen back before playoffs, which isn't horrible considering the recent play of Adam Brooks, the pickup of Riley Nash (and Foligno, another capable center), & center Suomela.
Basically for Andersen to come back before playoffs, I'm pretty sure the Leafs would have to either place Hyman on LTIR for the rest of the regular season or trade Pierre Engvall.