Besides to very good advices posted in other answers to this question; I want to mention a few words.
Can a masters student apply for a second masters in the same field at
I think, you are asking about applying and then studying for a second same masters degree. Because a student may be free to apply for a degree, but the admissions office will reject his profile as he is currently student else where.
Answer to your question depends on the educational system of the country and universities policies too.
In some countries, studying simultaneously in two universities and majors is prohibited and graduate students are only allowed to study in their own university. Also, I have seen many universities asking students whether they are currently students or not, because they seek full time students not part time ones.
However, I have seen that some students with outstanding grades and educational background can apply a minor very close to their field in their own university but it was for bachelors level only.
Also, you may find a university which accepts students seeking for double major; but the university in which you are currently studying may not agree to you to study a second major when you are their students.
As a general advice, double check the regulations of both universities and the countries in which you want to study simultaneously.