I think I'd shop for 10mm magazines.
The limiting factor is the design of the pistol. The 1911 was designed for the .45 ACP round. The maximum C.O.L. for the .45 ACP according to SAAMI is 1.275". I can't recall any loading data calling for longer than 1.270", so let's regard 1.275" as the outside limit.
At the other end of the caliber war debate, the 9mm Luger has a maximum C.O.L. of 1.169" -- and 9mm magazines typically have a spacer up the spine of the mag tube.
Both the .40 S&W and the .357 SIG are even shorter than the 9mm. The .40 S&W (per SAAMI) has a minimum C.O.L. of 1.085" and a maximum of 1.135". The .357 SIG has a minimum of 1.110" and a maximum of 1.140". Unless the .40 S&W mag spacer is a LOT thicker than the 9mm spacer, it would appear that the .40 mags should work.
But I'm guessing.