The spell Find Steed allows you to cast a spell and have it also effect your steed.
While mounted on your steed, you can make any spell you cast that
targets only you also target your steed.
In the targets section of the Players Handbook it states:
A spells description tells you whether the spell targets creatures,
objects, or a point of origin for an area effect. (PHB, pg 204)
With the spell Find Familiar, its description clearly denotes that you are the target:
You gain the service of a familiar, a spirit that takes an animal form
you choose: bat, cat, crab, frog (toad), hawk, lizard, octopus, owl,
poisonous snake, fish (quipper), rat, raven, sea horse, spider, or
weasel.
The spell indicates that you can’t have more than one familiar at a time, however in this case that would not be the result.
The PC casts Find Familiar and its effect targets the PC and (as per Find Steed) also targets the summoned steed. Tada! Two familiars appear, one bonded with the PC & one bonded with the steed.
Who controls the familiar bonded to the summoned steed, the GM or the Player?
Note: A Paladin with the ritual casting or magic initiate feat would be able to gain access to both spells, Find Steed & Find Familiar.
Best Answer
This does not work.
The spell Find Steed allows you to cast a spell and have it also affect your steed.
In the targets section of the PHB, it states:
In the case of the spell Find Familiar, its description denotes that the target is also an unoccupied space within range:
So the ruling that makes the target self spells transferable,
does not enable you to cast Find Familiar on your steed.