"so/as does Jim and Tom" OR "wso/as do Jim and Tom"

So is not idiomatic here unless it starts a new sentence, or at least follows a distinct break such as a semicolon or a dash.

Jim and Tom are two people, so the plural form of the verb is required.

I like it; so do Jim and Tom.

As only requires a comma, but it sounds rather formal.

I like it, as do Jim and Tom.

Try swapping the order of your sentence to see how the verb naturally changes. Instead of putting the names at the end, try saying "Jim and Tom do too." Since you'd never say "Jim and Tom does too," you know that "do" is the correct choice for a plural subject. If you're still unsure, a great trick is to replace the names with a pronoun. If you used "they" instead of "Jim and Tom," you'd say "as do they" or "so do they." You wouldn't say "as does they." This confirms that once you have more than one person, you have to move from the singular "does" to the plural "do." Keep in mind that using "as" or "so" in this way can feel a bit stiff in casual conversation. If you want to sound more natural when chatting with friends, it's often easier to just say "Jim and Tom like it too" or "Me too, and so do Jim and Tom." Just remember that the verb always has to match the people who follow it. If it's one person, use "does." If it's two or more, use "do."