Peptic Ulcer Disease: The patient's symptoms of constant, pleuritic right hypochondrium pain could be indicative of a peptic ulcer, especially if the pain is related to eating or worsens with certain foods. The location and nature of the pain, along with the demographic of a 58-year-old male, make this a plausible diagnosis.

Gallbladder Disease (Cholecystitis or Cholelithiasis): Right hypochondrium pain is a common presentation for gallbladder issues, especially if the pain is postprandial or radiates to the right shoulder.
Hepatitis: Inflammation of the liver could cause right upper quadrant pain, and while it might not typically be described as pleuritic, the location and constant nature of the pain could align with hepatitis, especially if there are other systemic symptoms like jaundice or fatigue.
Pneumonia or Pleurisy: Given the pleuritic nature of the pain, a pulmonary cause such as pneumonia or pleurisy affecting the right lower lobe could be considered, especially if there are respiratory symptoms like cough or shortness of breath.

Myocardial Infarction: Although less common, myocardial infarctions can present with atypical pain, including right-sided chest or abdominal pain. Given the potential for severe consequences if missed, it's crucial to consider cardiac causes, especially in a male of this age group.
Pulmonary Embolism: Similar to myocardial infarction, pulmonary embolism can present with sudden onset of pleuritic chest pain and is a life-threatening condition that must not be overlooked.
Hepatic or Splenic Infarction: These conditions can cause severe, acute abdominal pain and are medical emergencies.

Hepatocellular Carcinoma: While rare, a new onset of right upper quadrant pain in an older adult could potentially be related to a liver tumor, especially if there are risk factors like cirrhosis or hepatitis B/C infection.
Diaphragmatic Hernia: A rare condition where part of the stomach or intestine bulges into the chest through an opening in the diaphragm, which could cause pleuritic pain if it involves the right side.
Intra-abdominal Malignancy: Other rare abdominal malignancies, such as pancreatic cancer or metastatic disease to the liver or peritoneum, could also present with non-specific abdominal pain, including right hypochondrium pain.