Primary Aldosteronism: This condition, characterized by the excessive production of aldosterone, leads to sodium retention, water retention, and thus hypertension. It also causes hypokalemia (which can be associated with hypomagnesemia) due to increased potassium excretion in the urine. The hyponatremia might seem counterintuitive but can occur due to the complex interplay of hormones and fluid balance in the body, including the potential for a mild decrease in sodium levels despite overall sodium retention due to increased water retention.

Liddle Syndrome: A rare genetic disorder leading to excessive sodium absorption and water retention by the kidneys, causing hypertension and hypokalemia. While less common than primary aldosteronism, it shares some similarities in presentation and could potentially lead to hyponatremia in certain contexts due to water retention mechanisms.
Cushing's Syndrome: Excess cortisol can lead to hypertension and hypokalemia. Hyponatremia can occur, especially if there's significant water retention or if the syndrome is due to ectopic ACTH production, which can also affect other electrolyte balances.
Congenital Adrenal Hyperplasia (CAH): Certain forms of CAH can lead to an overproduction of mineralocorticoids, causing hypertension and hypokalemia. Hyponatremia might be less common but could occur depending on the specific enzyme deficiency and its impact on steroid hormone production.

Pheochromocytoma: Although typically associated with hypernatremia due to catecholamine-induced vasoconstriction and potential volume contraction, in some cases, especially with paragangliomas or certain genetic syndromes, there can be presentations that include hyponatremia. The critical aspect is not to miss this diagnosis due to its potential for severe, life-threatening hypertension.
Hyperaldosteronism due to Renal Artery Stenosis: Similar to primary aldosteronism but secondary to decreased renal perfusion, leading to renin-angiotensin-aldosterone system activation. This condition can cause hypertension and electrolyte imbalances, including hypomagnesemia and potentially hyponatremia in complex cases.

Gordon Syndrome (Familial Hyperkalemic Hypertension): Characterized by hypertension, hyperkalemia, and normal to low aldosterone levels. While it typically presents with hyperkalemia, there are instances where the electrolyte imbalance can be more complex, potentially leading to hyponatremia and hypomagnesemia in specific scenarios.
Apparent Mineralocorticoid Excess: A rare condition where there's an impairment in the metabolism of cortisol, leading it to act like a mineralocorticoid, causing hypertension and hypokalemia. Hyponatremia could potentially occur due to the complex effects on fluid and electrolyte balance.