First of all, if you take thyroid replacement medicine, it probably says that you should avoid supplements containing calcium, zinc and iron for 4 hours because it inhibits the uptake of the thyroid medication. Check for those little stickers on your prescription bottle, but if they aren't there, talk to your pharmacist anyway.
Secondly, mixing and matching vitamins is a job for food scientists, not for consumers. The ratios are extremely important, so if you take too much of one thing or too little of another, or if you are leaving out key ones, they will not be usable by themselves. That's why many doctors (who are not even nutrition experts themselves) refer to standard vitamins as "expensive urine" - most of it is eliminated. The vitamin industry took off about 25 years ago with the micronutrient model - individual bottles of vitamins and minerals. It was beneficial for the companies, but the consumers lost a ton of money. And we have an unprecedented health crisis. So that model has been abandoned by the more advanced scientists, with the focus being on cellular level nourishment.
You'll hear of people taking a multi and then adding a little of this and a little of that because of what they read in a magazine, but there is little or no evidence that this method works. And that's if you know where and how the products were made, which you usually don't. It makes no sense to take a supposedly complete product and then add to it with a few more things. What's the science behind that?
The key to vitamins is that they are not to be taken alone, or even in the standard "multivitamin" complex. Pills are not particularly absorbable (maybe 15-30% depending on how they are made), most over-the-counter combinations are not bioavailable (don't survive digestion or the opposite, aren't dissolved, so they pass right through the digestive tract nearly whole), and they are not synergistically blended. The same way calcium requires Vitamin D for absorption/utilization, most essential nutrients require others.
I have hypothyroid disease and also had bruising and low energy, and I spent a fortune doing all of the above. Once I got into the food science field, I learned what I was doing wrong and switch to comprehensive cellular nutrition. I got far better results and wound up saving money over all those fistfuls of pills.