Exist a M60 with a 120 mm gun Turkish Sabra further evolution of the Magach 7 retired in reserve in Israel Army but him have a 105 mm
Sabra
IMI 120 mm gun
Magach 7
Would be a great upgrade but would have to get Taiwanese production rights
GDLS once also offered a rebuild for M60's the M60-2000 though they would need a new turret. that is expensive.
Which took Abrams tech and integrated it into M60 but it never went anywhere.
There was also the 120S which was basically a Abrams turret on a M60 hull again never went anywhere. And the whole reason the Taiwanese are are looking to rebuild there M60A3 and presumably other Patton series Tanks is they can't get Abrams.
Basically the smaller the rebuild the easier. If it can be done in Taiwan then it's the better option.
There is also
An M60 with a modular armor package mounted to it including ERA, updated firecontrol systems and At the heart of both the Raytheon and M60 Pheonix offerings is the RUAG 120 mm L50 smoothbore gun
This same gun was used in the Falcon unmanned turret series developed by Jordon.
It's spec'd to fit in the space of a 105mm gun while still being lightweight and firing modern 120mm NATO standard ammo. At 6m although it is longer than the L44 (5.28m) found on Abrams yet shorter than the L55 (6.6m) or the french GIAT CN120-26/52 (6.24m).
It would be a smart move to try and either buy or licence this gun for a upgunned M60.
Frankly The M60 is long in the tooth, It can be brought up to a more modern standard but to do it it needs a total overhaul. New power pack, updated suspension and tracks, New main gun, updated armor package, new Fire control system. new optics ( driver).
It's not impossible just that it needs a bit of a investment. The Taiwanese have made an Investment in these Tanks after all they have rebuilt there M47 and M48 Pattons a number of times as well.
Now we know that the Taiwanese have elected not to accept these packages, and instead contract to the National Chung-Shan Institute of Science and Technology, Which is a State owned entity.
Hopefully for them they have some smart people who can come up with a good refit.
maybe even borrow from other refit offerings. the L3 Communications External Suspension arms, AVDS-1790 engine rebuild kits
Raytheon's, Fire controls, Electrical.
and of course a 120mm main gun.
with Engine and suspension upgrades the tank can then take the added weight of modern armor options. like the Sabra's ERA or Composite with Slat armor around the sides and Power pack.
Whatever the case M60A3 still has some life but the other 2 the M47 and M48 are past their useful lives. The Taiwanese CM11 and CM12 have already swapped to M60 hulls. might as well finish the job.
less dangerous than a true war 
