Easiest scenario:
Linguists relax their requirements of what qualifies as a language ...
Seriously, there is a wide variety of possible scenarios. Unfortunately, you didn't specify whether you prefer the existing languages to ramify ...
or extinct languages to be conserved in some form ...
or new languages arise where there was none IOTL.
There are good chances for each of these.
Let me point out two ideas by which you would gain a lot of languages at once:
1. No Germany.
"The Germans" as a nation arose very differently than many others; it is basically a union of several quite different Germanic tribes (which, a couple of centuries earlier, also came about as combat alliances between small tribes). Becoming one people was a process that took place in many individual relations roughly from 700 to 1100; but there are two kings that played a major role in this unification. This makes the process vulnerable to AH
.
These two are
- Charlemagne,
- Otto the Great.
In particular, if Otto doesn't manage to gather armies from all tribes, or perhaps even if he only loses against the Hungarians, power would fall back to the tribal dukes, and the Kingdom of Germany would become as theoretical as the Italian one.
This is relevant here not because German language would diverge in lack of a political link. It would lead to roughly half a dozen different languages instead of OTL's German because these tribal idioms already
were languages¹). IOTL, they only converged to one because of the intensive mutual contact.²) So, let the tribal duchies wage a lot of war against each other, or create more intensive links from them to other peoples (French/Danes/Italians/Hungarians/Czechs/Vinds/Poles). This should shift their focus.
2. More Germanic languages in colonies.
I'm aware of only two Germanic languages that arose in a European colony (in a wide sense):
Africaans (from Dutch) and
Pennsylvanian Dutch/"Amish" (from German).³)
There must be plenty of possibilities to create more, starting from a surviving Vinland.
The example of Pennsylvanian shows that the settlers with a Germanic language needn't be the masters of the land, they only need the opportunity to settle there. Then they need either
a) a strong motivation to stay among themselves (as OTL's two examples), or
b) become the majority in a region.
Connection with the colonial motherland (if any) may even prevent the formation of a new language: American/Australian English, and American Spanish are usually considered the same language as their European correspondents.
¹) Today's linguists tend to count all of them as one language, often even with the inclusion of the neighboring minority idioms, Langobardian (Italy) and Western Franconian (France).
There are good arguments for this; but the particular case of Old Saxonian (Northern Germany) is hard to define as the same language as, say, Bavarian, at least if you don't know the future development. From my point of view, Old Saxonian and Old Bavarian around 800 AD are comparably different from each other as Italian and Spanish today.
At least, I suppose, one can safely claim that they were standing on the sill to becoming individual languages.
²) While I'm at it: Dutch did not diverge from German. It just converged a bit less to the idioms now called German than those themselves. Politics is often irrelevant: The system of two languages Dutch - German had come to a clear end before the Dutch Independence.
At least that's my understanding - contradicting arguments welcome.
³) No, I don't count the settlement of Iceland as a colony any more.