Multistage valve system for multidose bottles

An apparatus for dispensing fluids, comprising:

• a manifold;
• a fluid path at least partially disposed in the manifold, the fluid path comprising an inlet and an outlet;
• and
• a multistage valve at least partially disposed in the manifold, the multistage valve comprising:
• a core positioned in the fluid path between the inlet and the outlet;
• a seal positioned around the fluid path between the inlet and the outlet, the core nested with the seal;
• a biasing device oriented to cause a first force to be exerted on the core, the first force biasing the core in a first direction against the seal to close the fluid path;
• and
• a plurality of diaphragms positioned adjacent to the fluid path, wherein the plurality of diaphragms is configured to act upon the core in response to fluid pressure on an inlet side of the fluid path exerting a second force against the plurality of diaphragms to at least partially unnest the core from the seal.