Once you've picked a subclass option at level 3, could you later take a different subclass option, or do you lock into a specialty at level 3 and then run with it for the rest of that class' progression?
For example, as a rogue, if you took the "Thief" archetype at level 3, giving you access to Fast Hands and Second Story Work, could you then take the "Assassin" archetype to give you the specific benefits that archetype gives instead of the "Thief" ones?
The PHB rogue description seems to imply that you couldn't:
At 3rd level, you choose an archetype that you emulate in the exercise of your rogue abilities: Thief, detailed at the end of the class description, or one from another source. Your archetype choice grants you features at 3rd level and then again at 9th, 13th, and 17th level.
but I'd like a more certain answer, especially one that refers to archetypes in general. Also I'm not ashamed to admit I'd prefer a source with some authority that tells me you can mix and match, but I am looking for the truth of the rules when all is said and done…
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Different to Can you multiclass the same class twice for different class features because the no on that demonstrates that you can't re-take a level of the same class. Taking different features for different levels is not the same thing, and would work differently.
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Similar to Can I mix monk traditions? but that one was specific to monks – which is why it didn't show up on any searches I did, and why it wouldn't on the searches of others. This question is specific enough to be clear and precise, but broad enough to be useful to others who aren't in the exact same situation/using the same class.
Best Answer
Short answer, you're locked in.
You can only choose one archetype per class, and there are no current rules that allow you to pick-and-choose features from different archetypes.
If you want to diversify your character's build, you can look into multiclassing. This lets your character pick up levels and features from different classes.
Note: You cannot multiclass into the same class to get additional archetypes (relevant Sage Advice).
I would recommend taking a read of this article: Modifying Classes. Whilst it doesn't discuss exactly what you're after, it might help. Specifically, the part on Creating New Class Options.
One way to get what I think you're after is to create a new Roguish archetype. It's a bit of a cop out, but with your DMs blessing it would definitely work. You'd have to come up with a very strong reason why your class would be meshing two existing archetypes (Thief & Assassin) though; and from a balance perspective you could come across certain situations where your character has too many tools at its disposal compared to other PCs which stuck to a single class option. Once again, discuss with your DM.
Back to the article, the key takeaway is this:
If you get an okay from the DM to create your Thiefsassin, you could utilise the Thief features for 3rd and 9th level, and the Assassin features at 13th and 19th level.