Usually yes — plain Mucinex (guaifenesin) and Tylenol (acetaminophen) work differently and aren't expected to interact, but the catch is that many "Mucinex" combo products and cold/flu remedies already contain acetaminophen, so check labels, stay under the daily limit, and ask your pharmacist.
Plain Mucinex is guaifenesin, an expectorant that thins mucus in the airways so you can cough it up; Tylenol is acetaminophen, a pain/fever reducer. They act by different mechanisms and aren't generally expected to interact, so plain guaifenesin is commonly taken alongside acetaminophen. The real hazard isn't a drug interaction but accidental acetaminophen overdose: many "Mucinex" combination products (such as Fast-Max and Cold & Flu lines) and many other cold/flu remedies already contain acetaminophen, and MedlinePlus warns not to take more than one acetaminophen-containing product at a time. MedlinePlus also cautions to check nonprescription cough and cold product labels carefully before using two or more products at once, since they may share active ingredients and cause an overdose. NHS similarly warns not to take paracetamol (acetaminophen) at the same time as other medicines that already contain it, such as cold and flu remedies, because you may take too much.
Before combining, read the active-ingredient list on every product: if your Mucinex already lists acetaminophen (or APAP), do NOT add separate Tylenol. Keep total acetaminophen from ALL sources under 4,000 mg in 24 hours (many clinicians suggest staying lower, around 3,000 mg) — MedlinePlus warns that too much acetaminophen can cause liver damage serious enough to require a transplant or cause death. Avoid or limit alcohol; do not use acetaminophen if you have three or more alcoholic drinks a day, and ask a doctor first if you have liver disease. Watch for signs of acetaminophen overdose (nausea, vomiting, loss of appetite, right-upper-abdomen pain, yellowing of skin or eyes) and seek emergency care immediately if they occur — overdose treatment works best when started early. Ask a pharmacist before combining if you take other prescription or OTC medicines, are pregnant, have liver or kidney problems, or are dosing a child, since pediatric cough-and-cold combinations carry extra risk.
This is general reference, not medical advice, and not a guarantee of safety. Interactions depend on your doses, health conditions, and other medicines. Always confirm with your pharmacist or doctor before combining products, and follow the dosing on each label.