Can you misty step while holding someone

Teleportation spells state when they permit a passenger.

Let's compare three spells.

Índice Show

Teleportation spells state when they permit a passenger.
Range "self" is a red herring.
Can you carry someone while Misty stepping?
Can you cast Misty step while restrained?
How often can misty step be used?
Can Misty step escape grapple?

Thunder Step
[...] You can also teleport one willing creature of your size or smaller who is carrying gear up to its carrying capacity. [...]

Thunder step explicitly states that you may bring along another creature.

Dimension Door
[...] You can also bring one willing creature of your size or smaller who is carrying gear up to its carrying capacity. [...]

Dimension door explicitly states that you may bring along another creature.

Misty Step
Briefly surrounded by silvery mist, you teleport up to 30 feet to an unoccupied space that you can see.

Unlike thunder step and dimension door, misty step makes no mention of bringing a long a passenger. Now, the rules for spells state:

Each spell description in Chapter 11 begins with a block of information, including the spell's name, level, school of magic, casting time, range, components, and duration. The rest of a spell entry describes the spell's effect.

The entirety of a spell's effect is contained within its spell description. In the case of misty step, quoted above, there are no effects that are not written in that description. Since the only creature mentioned is the caster, the only creature that teleports is the caster.

Range "self" is a red herring.

Amedeus' answer leverages the fact that the spell has a range of self to argue that you cannot bring along a passenger. This is a red herring. Lots of spells have a range of self and affect more than just the caster. So while their answer comes to the right conclusion, the reasoning given just does not support it. For example, consider the spell dream. It has a range of self, yet:

This spell shapes a creature's dreams. Choose a creature known to you as the target of this spell.

So having a range of self is not valid proof that a spell targets only the caster. Other spells which have a range of self and affect/target other creatures are:

detect thoughts
dispel evil and good
etherealness
eyebite
fire shield
flame blade
friends
gust of wind
pass without trace
produce flame
scrying
time stop
vampiric touch
wish
absorb elements
armor of agathys
banishing smite
blinding smite
branding smite
crown of stars
ensnaring strike
gift of gab
hail of thorns
investiture of flame
investiture of stone
lightning arrow
Melf's minute meteors
magic jar
primal savagery
searing smite
shadow blade
shadow of moil
spirit shroud
staggering smite
thunderous smite
wrathful smite
zephyr strike
Tenser's transformation
Tasha's otherworldly guise
speak with plants
guardian of nature
wrist pocket

So out of 76 spells with a range of only self, 42 (55.3%) of them affect or target more than just the caster. Therefore, "has a range of self" is not a reliable indicator that a spell targets or affects only the caster, in fact, it is the wrong conclusion for more than half of all spells having a range of self.

Can you carry someone while Misty stepping?

Since the range of Misty Step is self it only affects you and any belongings on your person. In conclusion - NO, as cool as it would be to do so, Misty step's range limits you to only teleporting yourself not other creatures (willing or no).

Can you cast Misty step while restrained?

Misty Step is not listed as one of the options in the Net rules for freeing someone restrained by the Net; only a strength check and damaging the net.

How often can misty step be used?

This ability is very interesting, allowing you to teleport 10 feet to an unoccupied space before each attack you make as part of an attack action. There is no limit to how often you do this, so you can bamf in and out of combat like you're Number Five. Bonus: Horizon Walkers also pick up misty step at 5th level.