It is possible to apply for the registration of a trademark in which a person has an interest, although this does not necessarily mean that the application will be successful, given that the Act stipulates a series of absolute prohibitions (Article 5 of the Trademark Act) and relative prohibitions (Articles 6-10 of the Trademark Act).
If a party wishes to register a famous or well-known trademark for a class in which it is not already registered, the owner of said trademark is likely to oppose any granting that they consider to be harmful to their interests.