Inclusion Criteria:  previous documented diagnosis of chronic SIAD  confirmed diagnosis of SIAD at screening visit defined as:  plasma sodium concentration 125 - 134 mmol/L, measured in lithium heparin plasma Plasma osmolality <300 mOsm/kg Urine osmolality >100 mOsm/kg Urine sodium concentration >30mmol/l Clinical euvolemia, defined as an absence of signs of hypovolemia (orthostasis, tachycardia, decreased skin turgor, dry mucous membranes) or hypervolemia (edema, ascites)  Exclusion Criteria:  lactose intolerance, celiac disease, milk protein allergy, soja allergy, nuts allergy or known hypersensitivity or allergy to one of the components of the protein supplementation (Whey Protein®, foodspring GmbH, Germany) inborn metabolic disorders implying carbohydrate, lipid or protein metabolism - severe symptomatic hyponatremia in need of treatment with 3% NaCl-solution or in need of intensive/intermediate care treatment at time of inclusion Risk factors for osmotic demyelination syndrome: hypokalaemia (K <3,4 mmol/L), malnutrition, advanced liver disease, alcoholism. contraindication for lowering blood pressure type 1 diabetes mellitus uncontrolled type 2 diabetes mellitus (defined as HbA1c >8.0%) uncontrolled hypothyroidism uncontrolled adrenal insufficiency reduction of eGFR <60 mL/min/1,73 m2 (KDIGO G3, G4 and G5) or end stage renal disease (dialysis) severe hepatic impairment (ALAT/ASAT >3x upper limit) or advanced symptomatic liver disease defined as past or current hepatic encephalopathy, liver cirrhosis Child C or decompensated (bleeding, jaundice, hepatorenal syndrome). treatment with a diuretic, a SGLT2 inhibitor or a corresponding combined preparation, lithium chloride, urea, vaptans, demeclocycline in the two weeks before screening. severe immunosuppression defined as leucocytes <2G pregnancy, wish to become pregnant during study period or breastfeeding end of life care Inability to follow the procedures of the study, e.g. due to language problems, psychological disorders, dementia, etc. Current participation in another intervention study lack of capacity or other reason preventing from giving informed consent or following study procedures.