Do spells that you get for free through your Muse count against the maximum number of spells known per each level (3)? Or can you have 4 spells known as long as it's given from your Muse?
Spell Repertoire
The collection of spells you can cast is called your spell repertoire. At 1st level, you learn two 1st-level occult spells of your choice and five occult cantrips of your choice. You choose these from the common spells from the occult list (page 311) or from other occult spells to which you have access. You can cast any spell in your spell repertoire by using a spell slot of an appropriate spell level.
You add to this spell repertoire as you increase in level. Each time you get a spell slot (see Table 3–6), you add a spell to your spell repertoire of the same level. At 2nd level, you select another 1st-level spell; at 3rd level, you select two 2nd-level spells, and so on. When you add spells, you might add a higher-level version of a spell you already have, so you can cast a heightened version of that spell.
Though you gain them at the same rate, your spell slots and the spells in your spell repertoire are separate. If a feat or other ability adds a spell to your spell repertoire, it wouldn’t give you another spell slot, and vice versa.
Abilities that add to your repertoire add to your repertoire. They don't restrict you to having the given spell be part of the same allotment.