The first thing to check would be whether the framework terms and conditions themselves give any steer on this point, as it is important not to do anything that contradicts the call-off process that is stated in the framework agreement itself.
Assuming the framework agreement is silent, we would then turn to Regulation 33(8(c)). This states that, where not all the terms governing the provision of the works, services and supplies concerned are laid down in the framework agreement, a call-off is to be made through reopening competition amongst the economic operators which are party to the framework agreement. On a strict interpretation, all suppliers would need to be invited to the mini-competition. However, an authority could choose to take a view that the issue of the EOI amounts to that invitation – and that if a supplier does not respond to the EOI, then there is no obligation to involve that supplier further in the mini-competition. It would be important if using an EOI in this way to make it clear that this is the invitation to the mini-competition, and that no further invitation will be issued to any supplier that does not respond.