A braking system for a vehicle includes: a brake input element for an actuation to input a brake pressure signal by a driver; a brake master cylinder coupled to the brake input element and supplied with hydraulic fluid from a hydraulic fluid reservoir fluidically connected to the brake master cylinder; and a first brake circuit. The first brake circuit has: a switchover valve with controllable through flow rate for the hydraulic fluid; a pressure regulating valve with controllable through flow rate for the hydraulic fluid; a hydraulic pump for optionally building up an elevated hydraulic fluid pressure in the first brake circuit; at least one first wheel brake cylinder exerting a braking torque on a first vehicle wheel coupled to the wheel brake cylinder; and a first fluid line from the hydraulic fluid reservoir being fluidically connected to the pressure regulating valve and to the hydraulic pump.