2004 Mercury Sable P0300 Multiple Misfire: Check Engine Light Flashes and Engine Stalls

I own a 2004 Mercury Sable and am experiencing recurring issues with the check engine light that comes on and off intermittently. A diagnostic scan shows a consistent P0300 code indicating multiple cylinder misfires. We have already replaced the spark plugs and performed an oil change, but the problem persists. Initially, the issue only appeared when the fuel level dropped below one-quarter, but now it occurs continuously. When starting the vehicle, the engine turns over but stalls immediately. After restarting, it runs briefly but then revs excessively and moves forward unexpectedly—despite being in park. During warm-up, it occasionally nudges forward as if trying to move. The code has been read multiple times and consistently shows P0300. We suspect a faulty throttle position sensor, though our recent inspection two weeks ago passed with no check engine light on. Any insights into potential causes or next steps would be greatly appreciated.