The relevant text is as follows.
Finally, when you Cast a Spell with a range of touch, your familiar can deliver the spell as if it had cast the spell. Your familiar must be within 100 feet of you, and it must use its reaction to deliver the spell when you cast it. If the spell requires an Attack roll, you use your Attack modifier for the roll.
The key is the phrase "deliver the spell as if it had cast the spell."
A familiar cannot cast spells. It has no spell slots, it knows no spells, and it cannot cast them to begin with. It cannot be counter-spelled, it cannot be targeted by Mage Slayer.
Therefore, it's sole capacity is to deliver touch spells as if it were the source of the spell, as a reaction.
This capacity does not, in any way, limit your own capacity. There is nothing in the rules supporting that; you still cast the spell, and the find familiar wording does not say anything about you. You're still prevented from targeting more creatures than can be targeted per general rules, but nothing more.
Therefore, both you and the familiar act as if they had cast the spell, you because you did and the familiar due to the spell description, and therefore you can deliver it to any target either of you can touch.