Would an Occultist who has the Necromancy Implement school and the Soulbound Puppet focus be able to use the Improved Familiar feat on his doll familiar puppets?
My first read is, yes, the Occultist would be able to:
From the rules - Prerequisites (for Improved Familiar): Ability to acquire a new familiar, compatible alignment, sufficiently high level (see below).
The Occultist with Soulbound Puppet does have a way of acquiring a new familiar. He can summon a new one after his old one expires in fact.
This also begs the question of whether or not more specifically worded feats like Improved Familiar Bond (i.e. specifically stating you need the familiar bond feature) work with the Occultist Souldbound Puppet. The text of Soulbound Puppet doesn't explicitly state that you have an arcane bond but it does say that you treat the puppet as a wizard's familiar which would require an arcane bond.
My thought on this is that Improved Familiar does work and more specifically worded feats requiring a class mechanic (like Improved Familiar Bond) do not. Any clarification would be appreciated.