Hydraulic safety system, brake system, and operating method

A brake system comprising:

• a brake master cylinder, which can be actuated by a brake pedal;
• at least one pressure chamber of which is separably connected to wheel brakes assigned to brake circuits, having a pressure control valve arrangement for one of closed-loop and open-loop control of a wheel brake pressure input at one wheel brake;
• a hydraulic pressure supply device that defines the at least one pressure chamber, the at least one pressure chamber is connected to the brake circuits by at least one separating valve and into which a piston is moved to build up pressure;
• wherein the at least one pressure chamber is of two-stage design with a first subchamber and a second subchamber;
• wherein the piston is first moveable in the first subchamber and then into the second subchamber during the pressure buildup and the first and second subchambers are hydraulically closed off from each other when the piston is moved a specified distance into the second subchamber;
• a reservoir for brake fluid;
• a first check valve defining a suction side hydraulically connected to the first subchamber and a blocking side hydraulically connected to the reservoir;
• a second check valve defining a second suction side connected to the second subchamber and a second blocking side connected to the suction side of the first check valve;
• and
• having an electronic open-loop and closed-loop control unit for controlling one of the hydraulic pressure supply device and of the pressure control valve arrangement.