Method for establishing a communication initiated by a sender terminal sending a communication request destined for a shared public identity which is associated with at least one first and one second destination terminal (12, 14), comprising the following steps implemented by the sender terminal: - a step of dispatching the communication request destined for the shared public identity, the communication request being received by at least the first and the second destination terminal, - subsequent to the reception (E6, E14) of at least one first provisional response to the communication request originating from the first destination terminal and of a second provisional response to the communication request originating from the second destination terminal, for each first and second provisional response received i. a step of obtaining (E70, E150), on the basis of the provisional response received, an address identifying the destination terminal which dispatched the provisional response received, ii. a step of dispatching (E8, E16) a discovery message in respect of the capacities of a terminal to said destination terminal on the basis of the address obtained, iii. a step of receiving (E11, E19) a response message in response to the discovery message in respect of the capacities of a terminal, originating from the destination terminal, said response message comprising the capacities supported by the destination terminal, - a step of retrieving (E72, E152) an item of information representative of the capacities supported by the first destination terminal and of an item of information representative of the capacities supported by the second destination terminal. - a step of dispatching the communication request destined for the shared public identity, the communication request being received by at least the first and the second destination terminal, - subsequent to the reception (E6, E14) of at least one first provisional response to the communication request originating from the first destination terminal and of a second provisional response to the communication request originating from the second destination terminal, for each first and second provisional response received i. a step of obtaining (E70, E150), on the basis of the provisional response received, an address identifying the destination terminal which dispatched the provisional response received, ii. a step of dispatching (E8, E16) a discovery message in respect of the capacities of a terminal to said destination terminal on the basis of the address obtained, iii. a step of receiving (E11, E19) a response message in response to the discovery message in respect of the capacities of a terminal, originating from the destination terminal, said response message comprising the capacities supported by the destination terminal, i. a step of obtaining (E70, E150), on the basis of the provisional response received, an address identifying the destination terminal which dispatched the provisional response received, ii. a step of dispatching (E8, E16) a discovery message in respect of the capacities of a terminal to said destination terminal on the basis of the address obtained, iii. a step of receiving (E11, E19) a response message in response to the discovery message in respect of the capacities of a terminal, originating from the destination terminal, said response message comprising the capacities supported by the destination terminal, - a step of retrieving (E72, E152) an item of information representative of the capacities supported by the first destination terminal and of an item of information representative of the capacities supported by the second destination terminal.