What's the maximum supported CPU?

To start things here be aware the Mini’s use a soldered CPU chip unlike 27” iMac’s (and only some 21.5” iMacs).

So you’ll need to replace the logic board assembly to properly repair this system. Mac mini Late 2012 ロジックボードの交換

As far as what are your options you are limited to what Apple used

• 2.5 GHz Core i5 (I5-3210M)
• 2.3 GHz Core i7 (I7-3615QM)
• 2.6 GHz Core i7 (I7-3720QM)

So why can’t I solder a new CPU chip: Given the number of solder pads (BGA) involved here you really need a proper chip rework station to preheat the logic board and lift the old chip off and then the reverse properly heating the chip and board as one of the killers is solder pad shear when the chip and logic board shrink at different rates causing the joint to fail. This gear is not cheap and there is an art to it as well. Unless you’re working with lots of boards its not worth it.