Acute Coronary Syndrome (ACS): This is the most likely diagnosis due to the nature of the pain described as "crushing," which is a classic symptom of myocardial ischemia or infarction. The intermittent nature could suggest unstable angina, a form of ACS.

Gastroesophageal Reflux Disease (GERD): GERD can cause chest pain that may be described as crushing, especially if it occurs after eating or at night. The pain can be intermittent and may mimic cardiac pain.
Pulmonary Embolism (PE): While PE typically presents with sudden onset dyspnea, it can also cause chest pain, which might be intermittent, especially if it's related to pulmonary infarction.
Pericarditis: Inflammation of the pericardium can cause sharp, stabbing chest pain that may be intermittent and can be confused with myocardial ischemia. The pain often improves with sitting up and leaning forward.

Aortic Dissection: This is a life-threatening condition that can cause severe, tearing chest pain. Although the pain is often constant, it can be perceived as intermittent if the dissection is propagating or if there are fluctuations in blood pressure.
Pneumothorax: A spontaneous pneumothorax can cause sudden, severe chest pain that may be intermittent if the pneumothorax is small and the patient's condition is fluctuating.
Esophageal Rupture: This condition can cause severe, constant chest pain but might be perceived as intermittent due to variations in pain perception or if the rupture is partial.

Hypertrophic Cardiomyopathy: This condition can cause chest pain due to outflow tract obstruction, which might be intermittent and related to exertion or emotional stress.
Chest Wall Syndromes (e.g., Tietze's Syndrome, Costochondritis): These conditions can cause chest pain that is often sharp and localized to the chest wall, which might be intermittent and could be confused with more serious conditions.
Mitral Valve Prolapse: In some cases, mitral valve prolapse can cause chest pain, which is often atypical and might be intermittent, but this is less common.