Associate one bid/opportunity with multiple accounts

Associate one bid/opportunity with multiple accounts

We work with building/construction contractors. Our scenario involves sending out a bid for a particular job to multiple general contractors who are all bidding on the same job (see illustration below). With the default setup, creating a $100,000 bid for each of 3 contractors (but for the same job) would show $300,000 in the pipeline, however it is really only $100,000 since ONLY one GC will be awarded the contract. We are trying to find a way to associate multiple accounts with one particular bid, so the pipeline analysis is correct. I know that this could be fixed on a report through grouping, but none of the built in analysis tools will reflect accurate information. Any suggestions would be greatly appreciated.

Example bidding scenario: