If there are more than 7 dimensions, nobody knows, and nobody cares, even the Commanders themselves. The Highest Command seems to be the one and only master of the Multiverse, and they're too busy acting as gods to undeveloped universes to form any religion of their own. Whether they are many or just parts of one entity, nobody knows. They share little information beyond simple facts. Whether they existed as they are from the beginning or formed as a consciousness combined from all the universes around them, nobody knows. One thing is known, that the Dimensions have existed for as long as the Highest Command has. If there are dimensions beyond the 7th, the general consensus among the 'verse's scientists is that it might not be dissimilar to the structure from the 3rd dimension up. Meaning that 8th is the "time" for 7th, and so on. If it's like that, there maybe be superiors even to the Commanders. A minority, however, regards the Multiverse as a loop. The entirety of the Multiverse is too big to encompass by anyone or anything, so it's entirely possible that somewhere, there is a tiny universe branch that loops back to the little smoke-filled room. Just like the experiments with time travel have allowed scientists to observe stable time loops in universe branches, the Multiverse may be a stable space loop, with no discernible end.
And speaking of space loops. It was found through experiment that every 3-dimensional universe is, technically, a closed infinite space loop. This allows the universe to recollect itself after the violent outburst that gave it life. When it happens, the universe suddenly reaches a state when it's exactly identical to its point of origin. Studies performed by the Alpha base have determined that when a universe timeline branch becomes sufficiently identical to another, they merge together and become one timeline again. For example, you're at a fork in the road. Two universes form when you decide to take either way, and if you weren't mauled by a bear on one of the paths, the two may rejoin again when you reach your destination. What will happen to the entire 'verse when it becomes identical to itself is a point of debate among scientists. Some speculate that the 'verse will loop back on itself, starting anew with essentially identical events. Others perceive this as a way new universes form, so that when one ceases to exist, another is immediately created in its place. There are supporters of the first theory, speculating that this was the reason for the Commanders' interference with our universe, and all others. If the Multiverse is such a closed loop, then it should become frustratingly boring for them, so they act as gods and influence people - playing games, essentially. That ours was the only universe given the knowledge to traverse the Multiverse is also explained thus, since there would be no way to know if we could actually breach into their dimension and mess things up somehow. Though frequently subjects of ridicule, the supporters firmly stand by their opinion.
(by this point you should realise that the Multiverse simply reflects my views on the world's structure, with an epic-like plot thrown in to keep it interesting)