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Do the levels in each class stack for the purposes of determining the strength of the familiar or are they two different kinds of familiars? Neither states they stack with other sources granting a familiar.
It all comes down to this language in the PRD under Familiars:
"Levels of different classes that are entitled to familiars stack for the purpose of determining any familiar abilities that depend on the master's level."
Some classes specifically reiterate that they stack (for example the Tattooed Sorceror's Familiar Tattoo specifically states that it stacks). The Tumor Familiar does not say anything one way or the other.
Most classes simply have a "Familiar". An Alchemist has a "Tumor Familiar". Is a Tumor Familiar the same as a Familiar? If the same, it stacks, if not, then I guess it doesn't (but then do you have two different familiars if you are a Wizard/Alchemist?).
My personal interpretation is that they stack. I see no problems with them stacking, it's less annoying than giving the player two familiars (one tumor and one regular) and I think it's the intent. Is it RAW, don't know. Is it intended by the Devs, don't know either. It's just the way I would play it.
Hope this helps.