What things can cause an increase in a person's 'demand' for levothyroxine???
All sorts of things.
So, assuming the optimum dose is taken in the recommended way in the morning without eating or drinking anything but water 30 mins either side of the dose (caffeinated drinks are a particular problem) -
Supplements - adding in too much iodine, developing low zinc or selenium levels (especially if you don't check when you switch to a new multivitamin or change supplements).
Increasing the amount of soya in your diet.
Starting or stopping any hormone treatment that contains oestrogen especially pills that are absorbed systemically, be it contraceptive or HRT.
Some medications that might affect absorption unless taken far apart from the T4 dose-
Any medication that affects stomach function such as antacids, or that empties the stomach very rapidly.
Medication that lowers cholesterol.
Iron & calcium supplements should also be taken well away from the T4 dose time.
Some medication info leaflets say they "may" be likely to cause an issue in untreated hypothyroidism - I think amitryptaline is one. Even when on adequate replacement T4 these just trying these drugs has often knocked my thyroid out in the past.
Some of us find we need to sometimes adjust down slightly for warm weather and once the weather turns again we need a slight increase.
Hormone imbalances, perimenopause & menopause can all cause changed demand for thyroxine. The latter two is often the onset of thyroid problems for women. My sister developed Graves within a couple of months of giving birth.
I am sure there are plenty of others. What might cause an issue for me might not affect you and vice versa.