According to the grammar bank in my English book, after "so that", I have to use subject + modal verb. But the very same book asks me to "complete the second sentence so that it has a similar meaning to the first sentence..."
What bothers me here is that there's no modal verb after "so that" in the book's sentence. What is the rule, then? If you know, please share it with me

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There's no rule about the verb type in the second half of the sentence when using subordinate clauses such as "so that...", "in order that...", etc.

We often use them with modal verbs, but often doesn't mean always! ^^
The only strict rule that you need to keep in mind is, as it's a subordinate clause, it acts to connect two sentences:

(Sentence 1) + so that + (Sentence 2)
Sentence 1: must describe an action/a cause
Sentence 2: must describe an expected result/an effect

For example:

1) "I’ll go by car so that I can take more luggage."
Action: going by car
Effect: being able to take more luggage.

But you absolutely could replace "can" by "am able to" (which is not a modal verb):
"I’ll go by car so that I am able to take more luggage."

2) "Complete the second sentence so that it has a similar meaning to the first sentence."
Action: completing the second sentence
Expected result: making it suggest a similar meaning to the first sentence.

Is it clear? ^^