Can a Catholic simultaneously profess more than one rite? Background

In catholicism, there are 24 autonomous particular churches sui iuris, one Western and 23 Eastern. All of these churches are in communion with the Pope, and thus are considered, for all intents and purposes, Catholic.  

When I was reading Orientalum Ecclesiarum, I was curious if there was no limit (other than 24) on the number of rites a Catholic could profess to be a part of.  The only statement I could find that implies "only one" was found in the 6th paragraph: 


  Finally, each and every Catholic, as also the baptized of every non-Catholic church or denomination who enters into the fullness of the Catholic communion, must retain his own rite wherever he is, must cherish it and observe it to the best of his ability...


However, nowhere is this papal decree could I find anything explicitly banning professing more than one rite.  Hence this lead me to the question...

Question

Could a Catholic believer profess as many rites as he or she pleases?  

Note: This is different from Can any catholic rite call themself Roman Catholic? because I am not asking about the validity of any one rite being equivalent to Roman Catholic, but rather the ability to profess differeing rites within Catholicism.
Other than biritual priests, who can "celebrate the liturgy and administer the sacraments in more than one rite," a Catholic belongs to one rite.

1983 Code canon 111 allows parents of different rites to choose which rite to baptize their children in:


  
  §1. Through the reception of baptism, the child of parents who belong to the Latin Church is enrolled in it, or, if one or the other does not belong to it, both parents have chosen by mutual agreement to have the offspring baptized in the Latin Church. If there is no mutual agreement, however, the child is enrolled in the ritual Church to which the father belongs.§2. Anyone to be baptized who has completed the fourteenth year of age can freely choose to be baptized in the Latin Church or in another ritual Church sui iuris; in that case, the person belongs to the Church which he or she has chosen.
  


Canon 112 governs changing rites:


  
  §1. After the reception of baptism, the following are enrolled in another ritual Church sui iuris:1/ a person who has obtained permission from the Apostolic See;2/ a spouse who, at the time of or during marriage, has declared that he or she is transferring to the ritual Church sui iuris of the other spouse; when the marriage has ended, however, the person can freely return to the Latin Church;3/ before the completion of the fourteenth year of age, the children of those mentioned in nn. 1 and 2 as well as, in a mixed marriage, the children of the Catholic party who has legitimately transferred to another ritual Church; on completion of their fourteenth year, however, they can return to the Latin Church.§2. The practice, however prolonged, of receiving the sacraments according to the rite of another ritual Church sui iuris does not entail enrollment in that Church.