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For lack of anything else on this, I assume the caster level for the SLA's an improved familiar has do not change as the master levels/progresses. Is there a way, without houserules, to increase the CL of the familiar?
Hit Dice: For the purpose of effects related to number of Hit Dice, use the master's character level or the familiar's normal HD total, whichever is higher.
A creature's caster level for SLA's is equal to its HD unless otherwise stated.
Since SLA caster levels are related to HD the level does increase.
The Improved Familiar I was looking at was the Imp. The entry in the SRD shows it having a CL of 6, but only 2 HD. Would this count as being "otherwise stated?" Would it stay at 6 even if it gains HD by becoming a familiar?
Also, where can I find the rule on SLA for HD? Assuming its buried in the monster rules somewhere, but I couldn't find it. Thank you for the help!
edit: Nevermind about the rules for SLA and HD, found that.
That would count as otherwise stated.
The familiar does not actually gain HD, it just counts as having extra HD for certain purposes. IIRC you have to be a 7th level caster to get an imp so by that time the imp will count as a 7th level caster.