Hi Kyle E,
Allocation rules under GL > Setup > Posting > Ledger Allocation Rule are designed to allocate balances of Main account or combination of main account and financial dimension only. In fact, this functionality is only applied before you close the books.
If the 3 entities are within AX, you can however create intercompany posting rules to post the share in expenses accordingly at the books of each entity .
The allocation will be manually computed though.
You can also do this via general journal or AP Invoice journal only. Hence PO invoicing is not covered.
You may do customization for the allocation rule if it is based on fixed percentge, fixed weight or fixed points.
Hope this helps :)