One way of handling this situation is to create characters as a group. Rather than coming to the table with your sheets already made, take a session and built the team together. It's easier to encourage diversity at the concept stage than to tell someone with a built PC that they have to start from scratch. Moreover, you can be there to ask questions like, "You've all built mages with one street sam — is he the bodyguard?" or "Your only source of magical healing is the paladin; does anyone want to roll a cleric or warlord?"
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.
Although, as mentioned here, multiclassing rules in PHB specifically 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.
And in Sage Advice
Can I multiclass into the same class to pick more than one subclass?
Multiclassing is designed solely for taking different classes. For example, you can be a fighter/rogue, but not a rogue/rogue.
(Just explaining to people that might get here to question the same thing and don't know why it is against standard rules, as mentioned in the text)
Hopefully, the books aren't everything
I know the same about specific official guidelines to multiple archetypes as you - I don't know any. And yet, I've created some NPCs and let my players create some PCs with multiple archetypes, although admittedly some turned out being broken. Anyway I might help:
- Create a mixed archetype that takes out some features from one archetype and adds from the other.
- Your scenario seems motivated by the background and race of the character, so it seems you want the most flavorish characteristics. From Wild Magic, you want Wild Surge and from Draconic Bloodline you want the Draconic Resilience.
- Balancing both of them together: If you give them the Tides of Chaos from Wild Magic as well, decrease the AC given by draconic resilience and don't give them the HP bonus. Also nerf some of the wild surge effects from the table as you seem fit.
- If you give them the full Draconic Resilience, don't give them Tides of Chaos. Honestly, I think Wild Surge by itself is not a "good" feature that actually needs to be balanced if you just give it for free. For example, casting a Fireball centered on yourself usually means killing yourself and half your party. There are enough negative effects already and its trigger is the DM wants to, so you can actually just give it for free and balance it through when you trigger it.
Personally, I would make them take the Draconic Bloodline archetype and just give the Wild Surge feature for free. Balance-wise it is does not seem broken to me, although I do have less experience with Wild Magic Sorcerers than almost every other subclass.
Best Answer
The problem is less one of classes and more one of roles.
If the party was playing full-on Wizards, it could essentially accomplish anything it wants through a mixture of Battlefield Control, Crowd Control, Damage Spells, and Save or Die Spells. This is because Wizards are incredibly versatile and can cover many different roles.
In general, your party will find itself in need of:
The lack of one or two capabilities can be challenging and interesting, the lack of all such capabilities simply makes a number of encounters nigh impossible.
Furthermore, all the party members will have the same weakness. A well placed Fear spell, and the whole party is running around, with nobody covering the others.
I would propose that you show your party a number of varied typical encounters, and explore with them how the party could possibly overcome the encounter, at various levels. If they are inventive and manage to surprise you and solve the problems, it may work. If they cannot figure out a way for over half the encounters, they are doomed.
The Same Game Test1 is a pretty useful resource for this; it "benchmarks" a character or party at level 5th, 10th, and 15th.
Let's start with level 5th:
I can see the party handling itself well against the Animated Iron Statue, Large Fire Elemental, Manticore, Centaur Archers, and Grimlock assault team.
How do they plan to deal with:
From the little information you gave, your party is more or less doomed. It can handle straight fights well, and that's it. Anything else, and it's a sitting duck.
Show them this test, show them how woefully under-prepared they'll be. Don't coddle them, show them how harsh reality can be straight from the first level, when they still have low-investment in their character. And be accommodating if they wish to switch.
1 See this answer by Hey I Can Chan for more links to the Same Game Test, including links to already run tests.