Mutual agency only exists for partners acting within the scope of normal business operations and dealings. For example, a retailer apparel partner with agency would not be able to contract the other partners into a deal to purchase a piece of investment real estate because this would be outside the normal operations of the business.
One of the retail partners can, on the other hand, purchase goods from a vendor and require the partnership pay for the goods. This transaction is within the normal course of operations of the business.