So to convert your requirements to CRM terminology, you want to be able to associate an opportunity with multiple organizations.
But you also want to track data relating to the nature of the relationships between those opportunities and organizations.
To do this, you would need a CRM that allows you to create custom modules and you'd need to create a module that tracks these "relationships". The resulting linkages would look like this.
Organization >> Relationship >> Opportunity
And this would allow MANY to MANY relationships between organizations and opportunities (deals).
Attributes of the relationship would be things like "status of bid", "amount bid" and similar.
You could use calculated fields in the Opportunity module to sum-up the total bids and similar.
You can't do this in Hubspot CRM (or Clearslide!!).
You could do it in any CRM that has it's own development environment (e.g. Salesforce, MS CRM, Sugar, Vtiger, Netsuite and others).
We have actually created this for project environments in our own Vtiger build (Vtiger is an open-source project). We call it our Stakeholder module.