The spell Phantom Steed, summons a creature that "uses the statistics for a riding horse". The Phantom Steed does have the extra benefit that it has a base speed of 100 feet, and that it does not tire (the latter is not in the spell, but can found in the DMG on p. 243, "Similarly, a phantom steed spell creates a magical mount with a speed of 100 feet that doesn't tire like a real horse.")
Under normal encumbrance rules, a riding horse can carry 480 pounds, easily enough for two medium-sized creatures with clothing. So, if needed two medium creatures could ride it, at least for a short time, for example one in the saddle, the other sitting behind or slung over. This also has been confirmed by the Q&A: Are there any rules or rule clarifications regarding multiple characters riding a single mount?. There possibly could be even more (if smaller or lighter) riders.
However the spell also says: "For the duration, you or a creature you choose can ride the steed." You or a creature would only be a single rider. So the spell states the steed behaves like a normal horse, meaning multiple riders are possible, and that only one creature (you or another creature) can ride it.
How many creatures can ride on the steed?
Best Answer
Just the one you designate
Phantom Steed says (emphasis mine):
Spells do what they say they do - except when they don't. It surely would be convenient if we could take this spell as written, where the only difference between a riding horse and a phantom steed was its speed. But in fact, most of the rest of the description of the spell is a list of exceptions, even if they are not explicitly called exceptions the way the speed is.
A riding horse has 13hp, and so does the steed - except that it disappears after taking a single point of damage.
A riding horse's equipment exists independent of the horse itself, and so does the steed's - except that it disappears if it is carried more than 10 feet away from the steed.
A riding horse is a creature, and can tire if ridden hard, for example in a Chase. A phantom steed is a creature - except that it cannot tire.
A riding horse yields 50xp if defeated, and so does the phantom steed - except that as a cast creature, it might yield no xp except those reflected in the awarded for defeating its caster.
Within this context, we understand that the steed has many differences from a real mount, even though its speed is the one one explicitly called out as an exception. When the spell says:
we then understand that this is yet another way the steed differs from a real animal (which can be ridden by anything physically able to do so). As an Illusion spell, you are in effect targeting a single creature, choosing for whom the steed will be real enough that it can be ridden, when it is not substantial enough to interact with anyone else. On the other hand, the creature you choose as the target could conceivably be one that could not actually ride a real horse, such as your war dog or even another mount.