Urinary Tract Infection (UTI) or Pyelonephritis: This condition can cause abdominal pain, diarrhea (due to the infection affecting the bowel habits), and renal calculi (kidney stones) can obstruct the urinary tract, leading to infection. Hiccups can be associated with severe pain or irritation of the diaphragm, which might be indirectly related to the severe abdominal pain.

Kidney Stones (Nephrolithiasis): While kidney stones are already mentioned, they can directly cause severe abdominal pain (renal colic), and the pain can lead to hiccups. Diarrhea might not be a direct symptom but can occur due to the body's response to pain or associated infections.
Gastroenteritis: This condition can cause diarrhea and abdominal pain. If the gastroenteritis is severe, it might lead to dehydration, which can increase the concentration of the urine and potentially lead to the formation of kidney stones. Hiccups could be a result of the gastrointestinal upset.
Inflammatory Bowel Disease (IBD): Conditions like Crohn's disease or ulcerative colitis can cause chronic diarrhea, abdominal pain, and potentially lead to kidney stones due to increased oxalate absorption in the gut. Hiccups are less common but can occur due to the overall distress of the disease.

Appendicitis: Although less likely to cause diarrhea, appendicitis can cause severe abdominal pain and potentially lead to hiccups due to the pain. If the appendix ruptures, it could lead to peritonitis, which might cause diarrhea. The presence of kidney stones could be coincidental.
Sepsis: Sepsis, especially from a urinary or gastrointestinal source, can cause all the mentioned symptoms, including diarrhea, abdominal pain, and potentially hiccups due to the systemic inflammatory response. It's crucial to identify and treat sepsis promptly.

Porphyria: This is a group of disorders that can cause abdominal pain, neurological symptoms, and potentially psychiatric symptoms. Some forms of porphyria can lead to neurological symptoms that might include hiccups, and there could be an association with kidney stones due to the metabolic disturbances in porphyria.
Familial Mediterranean Fever: This genetic disorder causes recurrent episodes of fever and acute inflammation of the abdomen, chest, or joints. It could potentially cause the mentioned symptoms, including abdominal pain and possibly diarrhea during flare-ups. Kidney stones could be a separate issue but are more common in patients with certain genetic predispositions.