Does a PF2e spellcaster who takes multiclass dedications into other spellcasting classes, and related spellcasting feats, gain more spell slots?

Question

Ezren is a level 10 evocation wizard, and hence would have spell slots of the following levels:

+-------------+-----------------+
| Spell level | Number of slots |
+-------------+-----------------+
|           1 |               4 |
|           2 |               4 |
|           3 |               4 |
|           4 |               4 |
|           5 |               4 |
+-------------+-----------------+

However, at level 2 Ezren took the Sorcerer multiclass dedication. At level 4 he took Basic Sorcerer Spellcasting, and Bloodline Breadth at level 8.

How many spell slots does Ezren have in a given day? Is it:

+-------------+-----------------+
| Spell level | Number of slots |
+-------------+-----------------+
|           1 |               6 |
|           2 |               6 |
|           3 |               6 |
|           4 |               4 |
|           5 |               4 |
+-------------+-----------------+

Because at level 8, spellcasting archetype feats grant an additional spell slot of first, second and third level, AND the bloodline breadth feat increases each of these by one?

Or do these sources of spell slots not stack for some reason? Coming from fifth edition, a wizard who multiclasses sorcerer still has the same number of spell slots as a pure wizard, so I'd like to clarify my understanding here.

Answer 1

You have two separate spell slot lists. This gives you

Wizard Spells    
+-------------+-----------------+
| Spell level | Number of slots |
+-------------+-----------------+
|           1 |               4 |
|           2 |               4 |
|           3 |               4 |
|           4 |               4 |
|           5 |               4 |
+-------------+-----------------+

and

Sorcerer Spells    
+-------------+-----------------+
| Spell level | Number of slots |
+-------------+-----------------+
|           1 |               2 |
|           2 |               2 |
|           3 |               2 |
+-------------+-----------------+

This gives you a total of 6 first, second, and third level spells, spread across different sources (so the slots aren't interchangeable, but there are still 6 of them)!

The Wizard spell slots can only cast spells from your spell book, and your Sorcerer spell slots can only casts spells from your sorcerers repertoire.

Relevant rules: Spellcasting Archetypes (emphasis mine):

... All spell slots you gain from spellcasting archetypes have restrictions depending on the archetype; for instance, the bard archetype grants you spell slots you can use only to cast occult spells from your bard repertoire, even if you are a sorcerer with occult spells in your sorcerer repertoire.

This means we have to look at the specific archetype for the restrictions, but the bard example gives us a pretty good idea of what to expect. So, looking at the Sorcerer dedication:

You cast spells like a sorcerer.

From Sorcerer's Spell Repertoire:

The collection of spells you can cast is called your spell repertoire.

So you can only cast spells from the archetype that are from your Sorcerer spell repertoire. It's a little round about reading to get unambiguous RAW (rules-as-written), but essentially multiclass archetype spell slots do not stack with other spell slots unless explicitly mentioned.