Putting a conventional alaskan (where the bar is held in the mill at both ends) on a 20" bar will restrict the cut by about 6" so the widest cut you will be able to make is ~14"
In theory it is possible to mill a log (by as you say making a cut on one side and then the other) that is the square root of 2 times bigger than the widest possible cut, so in theory the maximum diameter log that can be milled with a conventional alaskan will be 14*SQRT(2)=20"
However, in practice the bar clamps get in the way and don't permit the bar to do this on a log bigger than the max with of cut so the widest log you will be able to cut will be less than 20" in diameter, maybe only bearound 16" in diameter.
To improve this you have two options
1) Bolt the bar to the mill
This requires the the mill to be modified by cutting away the bar clamps and welding on a solid block of metal that can be drilled and tapped with a thread. Then drill holes in the bar and bolt the bar to the mill. This has other advantages as well, such as being able to remove the chain while the CS in on the mill, and being able to move the out board mill mount point to the middle of the bar nose (hole drilled thru the middle of the bar nose) . This will give you somewhere around 16" of normal cut width and allow you to tackle a 16*SQRT(2) = 22" diameter log
2) Use a single ended alaskan
To get a longer cut you can fit a one ended CS mill which will give you 17" of normal cut. However the bar clamp will still get in the way and cannot be removed such as is possible with the "double-ended bolt the bar to the mill alaskan" so it won't quite give you the Sqrt(2)*17" log diameter.
I personally don't like single ended alaskans as they wander around too much in the wood I cut and they cannot be used with bars more than about 25" long but I hear they go OK in softer woods.
This diagram might help explain it.
View attachment 330071
In practice I find turning the log is a PITA and it's just easier to use a wider bar.