By the rules you cannot. The rules for multiclassing state: With this rule, you have the option of gaining a level in a new class whenever you advance in level, instead of gaining a level in your current class. A subclass is not a new class.

Can you have multiple archetypes in 5e?

Using the books' rules, no, you can't.

You can only choose your archetype once, when you achieve that level (e.g. 3rd lvl Fighter). The only way to get another archetype would be leveling the same class from 1st level again, doing something similar to a multiclass Fighter/Fighter.

Can you change your subclass 5e?

D&D Now Allows Subclass Changes In Tasha's Cauldron Of Everything. ... One of the new options available in the upcoming Tasha's Cauldron of Everything Dungeons & Dragons sourcebook is the ability for players to change their subclass if desired.