A system for dispensing a mixture of a first product and a second product has a pump which presents a pump body that is intended to be connected to a bottle which contains the first product. The pump has a piston secured to a push button so as to be actuated in translatory motion in the body. The piston defines within the body a dosing chamber having a feeding inlet formed on a lower part of the body. The pump further has a lower check valve that is slidingly mounted in the dosing chamber between an upper opening position and a lower closing position of the feeding inlet. The system further has an additional container (attached to the body which is intended to contain the second product, an organ for opening the additional container being coupled with the check valve in order to, at least upon the first actuation of the pump, open the additional container by the movement of the lower check valve towards its closing position, the opening being configured for the mixing of the second product with the first product into the bottle.