Sure, you could experiment with going from 5 drops to 10 drops after a week. If it feels like too much, back off again or take a few days off to clear what's been displaced. Sometimes after a break you can resume at a higher level. You'll need to play with your dosing. Take magnesium, selenium, B-complex, and vitamin C to boost the good effects. Drink at least half your body weight in ounces of water with adequate salt to help keep your kidneys moving.
From what I've read here, everybody has their own experience. I look at iodine as a lifetime supplement. What can vary is how much I wanted in the beginning, versus how much I might stabilize with. I've been up and down with dosing, sometimes wishing there were hard-and-fast rules. You can write your own rules, based on your body's response, or you can go with Trapper's minimum of 100 mg, to some of the iodine docs recommending (and taking) 50 mg, down to the 12.5 mg that is close to what the average Japanese person is said to consume. Over time you'll sort out where you fall. :)
He has two versions, and both formulas are different from Lugol's. His SSKI is solely potassium iodide, and his SSKI 2% is potassium iodide with some molecular iodine added. With both versions you will get much more potassium iodide per drop than with Lugol's, and with the 2% you'll get half as much molecular iodine as from Lugol's 2%. He adds magnets to the SSKI 2% to make it more active in the body. It all comes down to which product(s) work for you, and figuring that out can be a lot of trial and error.