The wording of the Armorer artificer's Arcane Armor feature includes this phrase (TCoE, p. 15):
The armor […] also expands to cover your entire body, although you can retract or deploy the helmet […]
At level 9, you gain the Armor Modifications feature (TCoE, p. 17), which allows you to infuse multiple parts of the armor (chest, boots, helmet, and weapon).
So, before I get to level 9, can I wear magical boots and/or gloves? Or does my armor cover my hands and feet in such a way that I can't? Same for a magical helmet: can I wear one while my Arcane Armor helmet is retracted?
After I reach level 9, can I infuse (or find) a pair of gloves and put them on? Gloves aren't in the list of separate infusable armor parts. Can I find a pair of boots that aren't infusions and wear them?
I am assuming that when my armor covers my entire body, that's just for flavor, rather than a way to prevent me from being too awesome, and that the separate infusable parts are more for convenience … but you never know.
It's up to the DM to use common sense.
"Use common sense" is exactly the guidance given in the Dungeon Master's Guide (p. 141), under "Multiple Items of the Same Kind":
The Armorer Artificer's Arcane Armor feature says, in part (TCoE, p. 15):
To this DM, it looks like you would be functionally wearing boots and gloves, since the armor covers the whole body. As for a helmet, it seems there should be no issue wearing another helmet while your Arcane Armor helmet is retracted, just be careful not to engage your helmet while wearing another one.