Keep in mind that I'm relatively new to thyroid issues, but my impression is that the negative feedback system is similar to what's seen in the HPTA. With testosterone, it's not true that a small exogenous dose causes complete suppression. Your example of 25 mg per week would probably result in a modest amount of suppression, but still some endogenous production. The key takeaway is that exogenous testosterone seems to be more suppressive than endogenous testosterone. This means that a combination of endogenous and exogenous testosterone always results in lower serum testosterone than with endogenous or exogenous alone.
Let's look at some sample numbers: A normal guy starts with total testosterone at 600 ng/dL. He takes 25 mg T cypionate over each week. I'll arbitrarily say that the stronger exogenous effect is linear, and a factor of 2. The guy is taking 25 * 0.7 = 17.5 mg pure testosterone, which by my assumption is equivalent to 35 mg (2 * 17.5) of endogenous testosterone. Let's say that his natural production is 60 mg per week. Therefore he has suppressed natural production to 25 mg per week (60 - 35), while replacing it with only 17.5 mg. So his total testosterone drops to about 425 mg/dL. This is undoubtedly an oversimplification, but I think it does give an idea of what's happening.
So returning to thyroid, going by only
my numbers, it appears that exogenous T3 is only minimally more suppressive than endogenous T3, if at all; pre- and post-treatment free T3 are barely different. Rather, T4 is reduced by the amount needed to make the 10 mcg of T3 I've added exogenously.