In this inversion sentence, do I have to use "may" in the relative clause again? (Assuming you are not sure, that's why you are including "may" in your sentence)
"Robbery may not only take international students' possessions by an unlawful force, but it may also endanger the victims' lives.
Or
Robbery may not only take international students' possessions by an unlawful force, but it also endanger the victims' lives.
Which should I use?
Grammatically speaking, @anze-k is correct. For factual correctness, however, you need 'may' in the second instance but I'm not so sure you need it in the first. In your second example (which would need correcting to '... also endangers the ...'), you are saying that robbery definitely endangers victims' lives. This is not the case; robbery (for instance an unarmed robbery) is not definitely life-endangering.
However, robbery definitely does take possessions - otherwise it's only attempted robbery. You may want to reconsider using 'may' in that first part. Also, the unlawful force doesn't need an indefinite article.
Given the above, I'd consider rewriting the sentence to:
Robbery not only takes international students' possessions by unlawful force, but it may also endanger the victims' lives.
2nd may and it are redundant (we already know the subject).
Robbery may not only take international students' possessions by an unlawful force, but also endanger the victims' lives.
You have to independently determine if the "may" is necessary in each part of the sentence. As you know, "may" implies that an event is not certain, so only you can say (based on the context) if both events are uncertain. For example:
Due to the morning fog we may not see the sunrise, but we will see the sunset.
Due to the evening fog we will see the sunrise, but we may not see the sunset.
Due to the fog we may not see the sunrise, and we may not see the sunset.
Because of the ambiguity it's not always correct to omit a repeating "may", unless the meaning is obvious:
Due to the fog we may not see the sunrise, or the sunset.
In your example, if you want to emphasize that both are possible events, and not certain, there's nothing wrong with repeating "may". If brevity is your goal, you can, however, omit "it" from the second part, as the subject is the same, and also use "their" instead of "the victims'".
Robbery may not only take international students' possessions by an unlawful force, but may also endanger their lives.
As others have said, "may" is not really necessary in the first part, because it is a statement of fact, not conjecture. Using "may" only in the second part implies it is less likely than the first part:
Robbery takes international students' possessions by an unlawful force, and may also endanger their lives.
Of course, this makes the tone somewhat more ominous. It all depends on what you wish to say.
There is no rule that says you have to repeat the modal may. As a general, repeatable proposition therefore:
You may like this fact or you may not. [repetition]
You may like this fact or [may] dislike it. [no repetition, but repetition is implied]
However: two independent clauses joined by a conjunction may call for separate verbs depending on what you want to say.
1) "Robbery may not only take international students' possessions by unlawful force, but it may also endanger the victims' lives."OK
2) "Robbery may not only take international students' possessions by unlawful force, but it also endangers the victims' lives.
You can have "Robbery may not only" apply to both "take international students' possessions by an unlawful force" and "also endanger the victims' lives", but you can't drop just the "may" in the middle.
Also, you can't really drop the "not only" in the middle, either. If you want to separate out the two things it may do, you should move the "not only" to the front. So either
Robbery not only may take international students' possessions by an unlawful force, but it may also endanger the victims' lives.
or
Robbery may not only take international students' possessions by an unlawful force, but also endanger the victims' lives.
Note that the first has more of a sense of independence of the two possibilities than the second does. That is, if you want to say that one could happen independently of whether the other happens, the first would be better for emphasizing that, while if you want to emphasize the possibility of them happening together, the second one is better for that.
I don't see anything that resembles a relative clause in your examples. Neither do I see any inversion.
Your first example contains two complete independent clauses, each with an explicit subject and finite verb:
Robbery may not only take international students' possessions by unlawful force, but it may also endanger the victims' lives.
Here, "robbery" is the subject of the first "may", and "it" is the subject of the second.
You don't need the second "may", but without it the "it" has no role to play:
Robbery may not only take international students' possessions by unlawful force but also endanger the victims' lives.
In this version, the only subject/verb pairing is robbery/may. This is one clause with one subject and one finite verb. There are also two bare infinitive verb phrases: "take international students' possessions by an unlawful force" and "endanger the victims' lives".
The two bare infinite phrases act as coordinate arguments of the finite verb, effectively creating two verb constructions: "may take" and "may endanger".
Another option is to have two complete coordinate predicates:
Robbery may not only take international students' possessions by unlawful force, but may also endanger the victims' lives.
In this structure we repeat the "may" but we do not provide the second finite verb with its own subject. Instead, the coordinate pair takes "robbery" as the only subject it needs.
Your choice among these three grammatically sound options is a question of style, emphasis and intent.
