Posting more than one cost center in a transaction

We have a company where transactions in a ledger affect many cost centers.
For example:
If we withdraw from Bank A, we credit the Bank Account
Dr the Ledger, now under the Ledger there are cost centers that transaction goes into. Like Policy, Program, Region and Fund. All carrying same amount just to know how the fund was released and for what purpose, and the region or program affected.
The transaction can not be splitted because the amount was not shared between the cost centers. It is just to reflect in each selected cost center.
Can someone help out? Please.

If you do not split amount between cost centers, how do you get reports based on cost center? How do you maintain budget for those cost centers? Full amount can not be applicable to all cost centers.
And if you do not want any analysis based on cost center, just add a custom field for multiple cost center.

Thanks for your idea, but the splitting will not work in the sense that the account is a government account management.
The transaction is like Government can make budget of $5000, for a particular policy or program, to be spent on a geo-political region, funded by a government unit. if you split the transaction it will record the transaction into the number of split which will be over the real amount, but if the program allow you to select more than one cost center, it is that same amount that will be in all the cost center and because its going into a single ledger account it will only record the transaction once and that’s all.
Budget is not done in cost center in this case it is done on the GL, so your budget does not affect cost center, but you can see how it was spent on the cost centers.
If I could get a better idea on how the custom field will work I will appreciate that. We just need to achieve this.
Once again, thanks for your contribution.