The short answer is: Hungary does not limit the number of citizenships its citizen may hold at the same time. You can have Hungarian citizenship as your second or third citizenship. However, this does not automatically mean that you can hoard citizenships without consequences.
When you apply for Hungarian citizenship through regular naturalization, you need to pass an exam as part of the application procedure. During this Hungarian citizenship exam, applicants must demonstrate how well they know the history of Hungary and how public administration works.
Naturalization is the official term for obtaining citizenship. The more ties you have to Hungary, the sooner and easier you can become a citizen. However, eventually you become eligible even if your only tie is living here; that is when we talk about regular naturalization.