@the_jetset:
THREE TURN PLAYING SYSTEM and ENHANCED COMBAT
Attacking Together Casualty Selection

Axis and Allied forces that attack together randomly select casualties for the same unit type. (For example, if there are 3 German and 2 Italian infantry and they decide that an infantry will be the 1st casualty, the Germans roll 3 dice and the Italians roll 2 dice. Whoever has the higher sum takes the casualty.) Any other “random” method may be used as well

Occupation may be predecided. However, if the attacking players cannot agree: Country with the largest army remaining at the end of the battle takes control of the occupied territory.
What about something which doesn’t need any additional roll?
The greatest number of units takes the casualties and when you reach equal number of units, each nation pick 1 unit at a time, starting with the other friendly units.
Example: 5 UK and 3 US Infantry, and must take 1 hit, so you loose 1 UK Inf.
Next combat round, 4 UK and 3 US, suppose 2 hits, UK loose 1 Inf, US loose 1 Inf.
Next combat round, 3 UK and 2 US, suppose 1 hit, UK loose Inf,
Next combat round, 2 UK and 2 US remain, players agree which is the first casualty, then pick alternatively.
OR
You pick casualty according to a rough ratio between attacking nations:
around 1:1, the largest number is picked first, the other second, alternatively,
if even, both players should agree about who take first casualy, then alternate,
around 2:1, the largest number is picked twice first, the other take 1 casualty, alternatively,
around 3:1, the largest number is picked three times before taking the other once,
around 4:1 and above, 4 units are picked on the largest group, then 1 unit of the other.
Since this ratio can change each combat round, you apply accordingly to the actual ratio.
Example: 5 UK and 3 US Infantry makes 1.67 ratio, and have to take 1 hit, so you loose 1 UK Inf.
Next combat round, 4 UK and 3 US, ratio is at 1.33, nearer 1:1, suppose 3 hits have to be chosen, UK lost 2 Inf, US 1 Inf.
Next combat round, 2 UK and 2 US remaining, still 1:1 ratio, players agree which is the first casualty, then pick alternatively.
No special roll required, so when rolling dice in game, it stays focus on combat.
IMO, it is simpler.