You don't need a magical reason to solve this, here are a few
Magical items are made of heavy things. Only the strongest person can carry so many items ( and has little use or understanding because they spent the time studying trying to build their physical strength ). The only feasible way to do it is to carry them in a horse and cart at which point you aren't wearing them and there's no point
People would look at you funny if you had a lot of bling on, in society today overdoing it is frowned upon. Subtlety. Why not the same with magical items? Don't prevent having too many, just make the character a pariah when they do so
There are a lot of things within the range of weight that I'm able to carry, that are simply too unwieldy and bulky to carry. For example I can't carry a 10m x 10m cube of polystyrene. It's light enough for me, but it's too bulky. Make it the same for your magical items. Carrying more than 2 or 3 can be impractical purely from a volume/density point of view
Nobody really buys their magical items, they buy them with loans, and if you have too many loans, the interest prevents you from doing other things ( like eating )
Magical artifacts aren't seen as magical, they're seen as religious, divine artefacts. As such, they're gifted by clergy, and held on to for their power, seen as gifts. Some people see crucifixes this way, but they don't walk around with hundreds of them hanging from their neck. Additional crucifixes and prayer beads don't make Gods presence stronger around you, so why would more of these magical artefacts do that? These people believe their power comes from God/Gods not from an innate magical ability
There's another side, even if it's known that carrying multiple artefacts conveys more magical effects, and they are cheap, such actions may be blasphemous, or seen as greed. Equivalents of the religious texts we have that pour scorn on greed and materialistic tendencies may make hoarding magical objects obscene, possibly illegal
The destruction of a magical object may incurr a costly event, such as an explosion or the sapping of life force. While multiple of these objects would be powerful, the destruction or damaging of one may set all of them off, incurring a devastating event to the owner and all around them. This also provides you with a mechanism for Kamikaze Wizards, magical suicide bombers, etc
Perhaps a vital ingredient of constructing magical objects involves something that smells horrific. Perhaps it's a binding agent, or a catalyst which unlocks the powers of the items. Eitherway if you have too many items in one location, you're overwhelmed by the smell, it becomes unbearable, the weak of heart may pass out from the fumes.
This places those with no sense of smell at a huge advantage however
There are plenty of things we ingest on a daily basis such as caffeine that are poisons. Caffeine for example is a natural insecticide, insects eat a plant with caffeine in its leaves, and are unable to regulate their bodies and go into overdrive. They curl up into a ball violently shaking, super wired.
We're too big for caffeine to do that to us, and perhaps it's the same with magical items. Something in them is poisonous but within tolerable levels. Until they reach a critical mass and we start to lose the battle, leading to a slow decline.
Perhaps as a result, users with lots of magical items become weak, suffer signs of dementia, respiratory issues, etc
What if one of the traditional ingredients was radioactive? Perhaps they were using a mildly refined form in order to produce the heavy metals for aesthetic sake ( the bright red uranium dishes from early 20th century that were so popular? Or the glow in the dark watches that used Radium? ) Too many magical items mashed together may create a critical mass, resulting in dire consequences or radiation poisoning
Faced with a proliferation of magical items and a shortfall in government coffers, perhaps taxes were instituted on the growing trade in magical items. It's no longer financially feasible for people to own large numbers of items, and it makes sense for the rich to go for individual expensive powerful items rather than face a tax burden of multiple not quite as expensive items
It may be custom to prepare each item, a ritual of sorts, required each day. Owning more items means more time spent doing this, which becomes tedious and impractical
The maintenance costs of keeping the items operational, clean, and well functioning may make owning lots of magical items unfeasible
Magic can set a house on fire, but so can matches. Why carry an amulet that can set things on fire when a small box of matches will do the trick too? As technology progresses, things can be done better and more reliably with a machine than using magic, so people may be able to have lots of magical items on them, but there's no need.
Why carry a staff of light, a magical compass, enchanted music box, and crystal ball for communication, when you can carry an iPhone? Of course the lightning wand and the paper thin adamantium armour that melts attackers would stay