Foam dispensing system having multiple valves for a dispenser, and associated foam dispenser

A foaming product dispenser, comprising:

• a distribution system, comprising:
• an actuation head, comprising:
• a push button;
• a nozzle in the push button;
• and
• a cylinder attached to the push button;
• a fret, comprising:
• an outer decorative wall;
• an inner sleeve;
• a housing between the outer decorative wall and inner sleeve, wherein a portion of the actuation head is movable in the housing;
• a base, comprising:
• a bottom seated on the fret;
• an intake port in the bottom;
• and
• a rod extending from the bottom towards the actuation head;
• a deformable element attached to the fret and the base, forming a product chamber between the deformable element and the base and an air dosing chamber between the deformable element and the actuation head, the deformable element comprising:
• a flange controlling the flow of product into the product chamber through said intake port;
• a slot controlling the flow of product out of the product chamber;
• a lip controlling the flow of air into the air dosing chamber;
• and
• an annular lip controlling the flow of air out of the air dosing chamber.