Lets breakdown more on this and I will suggest different approach to your business process
1. Company A and Company belong to same corporate group ? if yes these will be mapped as company codes, Company C is vendor- this need not to be mapped in vendor master. (No need to map as company code).
2. User will create a PR for requirement directly in company B with account assignment U. (This means it can use MRP to create a PR or manually create a PR), then you create the RFQs (ME41) on the multiple vendors, Vendor will respond back with prices, I am assuming here Mark up price will be fixed and there will no process of getting approvals on e-mails
3. Maintain the prices for RFQs (ME47), You can setup on release strategy on RFQs for getting the quotes approved by any personal from company B (as you have common user master). The shortlisted Quote get approved ( You can add various levels relevant competent authority here too, in your case finance)
5. Create Stock transfer order with Mark up price (Document Type NB- You can create another document type too.) used in inter-company stock transfer process. You can also setup approval process for this document type too.
6. You create a Purchase order to fulfill the requirement with reference to approved RFQ. Buyer need to mention the account assignment C for sales order that created in Step (as you are no longer use account assignment U in PO). You also setup release strategy to get approval from various levels of competent authority.
I have skipped step 4 from your requirement as it is more on manual side-Company B then creates a sales offer with a markup and issued via email to Company A
5. Perform the GR w.r.t to PO in Company B-MIGO
6. Create Outbound delivery with Reference to Stock transfer Order-VL10B
7. Perform Post Goods Issue and Create Billing document on Company A-VL02N
8. Receive goods in Company A with Reference to Outbound Delivery (MIGO)
There may other solutions to same scenario that you can consider. But I think this approach you will less number to transactions and documents created in the SAP system.
I can also note that the PR you are creating in Step 1 in your approach is not getting close or ordered. if you follow your approach, how you will close the PR you created in Step 1 ?