The multiclassing rules (PHB, p. 163) state:
To qualify for a new class, you must meet the ability score prerequisites for both your current class and your new one […] Without the full training that a beginning character receives, you must be a quick study in your new class, having a natural aptitude that is reflected by higher-than-average ability scores.
Can the ability score prerequisite(s) for multiclassing be met by (long-term) use of a magic item(s) such as the Headband of Intellect (INT 19), Ioun Stones (+2 to various ability scores), etc.?
The phrase "natural aptitude" suggests nonmagical, but a character could have been using a magic item for years which seems virtually indistinguishable.
There is nothing in the PHB or DMG that I can find that indicates that this is not possible.
However, because of this fact, this is a conversation you need to have with your DM.
It's possible that in the campaign they envision, there would be severe complications, it's possible that there won't be. But only they can determine whether or not this is a good idea for your game.