Hi Alexander.
Here is a possible solution for you, but to have alternating groups of accounts it does depend on Sorting first by the Account and then by other data. If the data is sorted without sorting by the Account first, the matching account numbers will still share the same color even though they are not together. However, the account numbers in-between the formatted accounts would all be the same. In this case see the suggestion further down in this answer.
Here is the initial idea. Use a Helper column to get a unique list of the account numbers. I did this in Column H below with this formula.
=UNIQUE(B2:B13)
Then set up Conditional Formatting for every other account number. The formulas for these would be:
=$B2=$H$2
=$B2=$H$4
=$B2=$H$6
=$B2=$H$8
etc.
That will color every other Account Number in the unique list and leave the numbers in cells 3, 5, 7, etc. unformatted like this.

As I said above, if the data is not sorted first by the account, the account numbers that appear in cells H2, H4, H6, etc. would still be colored and each of those would match but none of the odd cells would be colored and would likely be next to each other in places like this.

If you are going to be sorting this way, I would think that it would be better to assign a different color to every account, but there may be too many to make that feasible.

Hopefully this helps to give some direction. Reply if you need something more specific.