Can we have additional contact fields within each customer. Merged

I deal with large companies that have several contacts. For example there may be 2 or 3 different departments that are asking us for quotations. Plus I then have their accounts department contacts for invoicing & purchase order infromation. 

At the moment I can only create 1 contact. Support have told me to enter in other email addresses into the customer email fields & then delete as appropriate. My accountant has advised me to create a new customer per department.  To be honest, neither is appropriate and both options are restrictive.  Surely I should be able to create more than 1 contact and this would be a great additional bit of information to be able to have.