I believe you can’t strap anything to it because power armor is supposed to be extremely bulky. Fitting a backpack around your arms while wearing it would be odd, to say the least, and even if you managed to get something around it, you wouldn’t have easy access to it.
It’s literally a giant suit of metal. You shouldn’t even be able to move without it being powered.
However, there IS a power armor hauling frame you can get that adds 120 volume. This can only be worn while wearing power armor, however. So if you find one before you have power armor, it’s kinda useless.
You could always just drag a shopping cart around with you, carrying various different killing instruments. Usually what I do for looting runs anyway.