There have been those who have said that Dionysos replaced Hestia on Olympos as one of the 12 great Olympians (I am not going to even get into how variations differed from region to region on what gods made up said set but rather deal with this solely). While there is no ancient textual support for this, I think that the tendency of people to want to exchange Hestia for Dionysos says something very profound in their relationship.
As I said in an earlier post, Dionysos is as the divine spark. We see this two in myths of his sacrifice where he is consumed by the Titans and that spark is handed down from him into each of us to create the divine spark of our souls. Yet we all know too that Hestia dwells at the center of all things, as does Zeus who dwells within and around all things. If we consider that Dionysos is part of Zeus (although is not Zeus at the same time anymore than Asklepios who is part of Apollon is Apollon) then we are still left with three beings of the center of all things. Zeus who dwells there by virtual that he is within all things as king of the gods and cosmos, and yet Hestia by merit that she is by necessity as the goddess of the hearth, that goddess who dwells there by reason that she feeds the fires that dwell within all things (although the assumption is that she is the living fire within all things, I think that this more accurate that in accordance with her actual cult that she sits in the center of all things much as she dwells in the center of Olympos, at Delphin and within each house for the purpose of tending the fires within. This makes her necessary to dwell at the center, and that no life could be without her presence there.
However if Dionysos is indeed the divine spark as is suggested by myth, that which is carried within all of us from birth and even through the passages of death, then it makes sense that Dionysos must dwell in the center, and may be that very attribute or part of Zeus that dwells within even as he is the genitive part of Zeus via the myth of his birth from the thigh of the god so near his reproductive organs. He is the seed of the life, germinating within all things, appropriate too for a deity associated with the mysteries of Demeter and Persephone. In which case we can see him too as described as the child of Haides. He is the spark of flame which Hestia nurturers. As such he cannot take her place at Olympos. Hestia essentially is Olympos, as her presence therein at the center gives life to the divine realm of the gods. There would be no Olympos without her. Just the same Dionysos dwells within Olympos as the divine fire of Olympos, the spirit of Olympos. For his first incarnation as Zagreus he was made by his father Zeus as king, and in such a fashion is united with Olympos even as his substance is united with all beings on the earth.
Yet we find Artemis at Olympos as that goddess which brings the hinds of her hunt which are received by Apollon (or in later traditions by Herakles who was said to have been given the duty by Apollon). We see Artemis and Apollon at Olympos as beings which feed and invigorate the halls of the gods. They are as nurse and caretaker of Dionysos as they are of Olympos, providing stability and even bringing happiness and joy by their activity therein (as we find Apollon in the poem of Kallimachus arriving among the company of the gods and by his song making all the gods merry and dancing happily). Dionysos too is credited with bringing much joy and happiness to the company of the gods, and his own substance being that which is preferred among the gods apart from all others. In other poems we have Apollon with the Muses being the first to greet Dionysos and making merry in his presence. Although Apollon and Artemis bring substance to Olympos, it is the presence of Dionysos, the ever dwelling flame of Olympos who is the spark of all source of happiness and merriment and by such is much beloved.
Such can be acknowledged in the relationship of the brothers, Apollon and Dionysos. Whereas Artemis after had a nurse like relationship, or nurturing relationship with him, even if at times being one of primal conflicts, the relationship of Apollon and Dionysos is which we overlaps. I would consider there that many of the overlaps deal with this very nature of Apollon and Dionysos acting together as is essential in nature. Dionysos dwells within civilization and the arts of civilization which nurture and inspire the soul into growth and development as the essential spark of this creative potential from the divine. Apollon acting with Dionysos brings forth these very same things. His music gives form to the fire. He is at the center, at the axis directing the movement of all things around it. His music is the influence upon the central spark, providing direction and informing upon it. He is the first celebrant, the bacchic one along with his twin Artemis. They dance about the divine spark as Hestia tends eternally to it. Essential and inseparable together as they weave their part of life and the cosmos, as Leto who is as night, the womb of life which gives birth to bring forth the light, even as Apollon and Artemis are of the twilight ushering in the light and as such part of its manifestation.
To them I tend them all I tend to the flames for the very heart of life.