The answer is unfortunately dependent on when and where you are asking this question about. Much of the work of the last forty years in medieval history has emphasized the peculiarities of local practice over any global medieval legal definitions of ritual practices of fealty. The sort of organized, systematic understanding of terms such as the French hommage or the German mannschaft proposed by Marc Bloch in the earlier part of last century has been forcefully challenged, first and foremost by Susan Reynolds in her Fiefs and Vassals: The Medieval Evidence Reinterpreted (1994). Reynold's main point, among many others, is that there is a difference between theory and practice, and, in practice, the act of commending oneself to a lord in homage meant a variety of different things. It could be for land, it could be for rights, it could be to resolve disputes, and it could be the prelude or resolution to violence. You could absolutely offer fealty to two different individuals or to the same individual twice for separate reasons.

The fact that a man could and did swear fealty to more than one lord often caused problems for both the lord and the one giving fealty. One of my favorite texts to teach this problem is the Conventum. Here I have linked the translation by Paul Hyams and Susan Reynolds mostly based on the edition by Jane Martindale. Written by Hugh of Lusignan in the early eleventh century, the Conventum tells the story of how Hugh entered into a long dispute with William, Duke of Aquitaine, over the ownership of several castles in Poitou.

There is a lot to unpack here, and the text is clearly biased on Hugh's behalf, but it also reveals the tensions embedded in a political landscape that lacks the structure of the state and, thus, is reliant on the strength of personal relationships. One part of the story directly addresses your question and should lend some clarity to the question of why someone would swear fealty to more than one person. In the 1120s, a conflict breaks out between Hugh and two other men, Aimery and Bernard, all of whom were fighting for control of Civray, a castle that we are told Hugh's father enjoyed a quarter control over. William intervened in the conflict and commanded Hugh "to become Bernard's man for the part of the fortress which had been his father's so that they could both prosecute the quarrel with Aimery together." Hugh complied, becomes Bernard's man, and pursues a conflict with Aimery of both William and Bernard's behalf. Soon, Hugh is betrayed, because William makes peace with Aimery but, although Hugh has preformed oaths of a sort to William, that peace does not extend to Hugh. Hugh continues to fight with Aimery and suffers some losses, since neither William or Bernard show any inclination to help him.

In the early eleventh-century France of the Conventum, the political landscape is a hodgepodge of agreements that Hugh has made to specific individuals for specific rights. Despite the fact that agreements tend to be broken with startling regularity over the course of the text, Hugh emphasizes that he complies again and again with William's wishes "out of love of the count and fidelity to him." Indeed, William's words reveal nothing of a ritual of homage—which is not to say it did not exist, but rather than for Hugh it doesn't seem to matter. For Hugh, the central binding principal seems to be an oath of fidelity to his lord. The public renouncement of parts of this oath by Hugh and the later (re)swearing of this oath are the narratological highpoints of the text. Both are public events and seem to be central to Hugh's conception of the proper world order. You could describe them as acts of homage—I certain have when teaching at times—, but just recognize that we are applying a word that Hugh, for whatever reason, doesn't himself employ.