At 1st level, a sorcerer, bloodrager, or any other character with one of the following bloodlines can choose to gain a bloodline familiar.
Officially, it's locked to only the listed bloodlines. But this is probably one of the easier things to homebrew.
Shapechanger? My gut reaction is to give them the ability to "change shape(su)" into one other form allowed as a base familiar. Whatever ability is chosen, it's meant to be pretty minor as just getting a familiar is the primary purpose of that option.
You'll find a lot of opinions on familiars. They can make fine scouts and some can serve other purposes like using wands, especially if you decide to take improved familiar.
A bonded object is really as much of a potential liability, as it can be taken or destroyed and you are way more impacted than if a familiar dies. You can take precautions to protect either, but also most GMs won't ever go after either.
You can get a bonded object with the arcane bloodline, but it's not that amazing for a sorcerer. One extra spell of your highest spell level, where you will often already be able to cast 4+ of those per day.
Regardless, you will have to enter homebrew territory for a shapechanger bloodline familiar. I'm not sure if you'd get a better response for ideas in the homebrew section. Hopefully your GM will be open to whatever homebrew you come up with. But keep in mind the bloodline bonus is intended to be fairly minor and focused on the familiar instead of the master.
As it happens Razmiran Priest and Crossblooded Sorcerer are archetypes that can stack with each other. This would give you a second bloodline that you could choose from one of the approved bloodlines. Not sure if this interests you but there you go.
That might work, but is questionable for stacking. Crossblooded alters the bloodline power and the bloodline familiar replaces a bloodline power. You can run it by your GM, and many would probably be fine with it, but RAW you can't combine those.
It doesn't matter if it's an archetype or not. The rules on stacking do start with archetypes, because that's the most common form, but it's really about "alternate class features".
But also, the archetype limitation is triggered from either direction. Bloodline familiar replaces the 1st bloodline power, which prohibits you from taking crossblooded, which alters bloodline powers.
Although the FAQ for crossblooded/wildblooded does bring up that allowing combos like this is up to "GM's purview", meaning house ruling this may not be a bad idea.
I’ll just point out that in the text of the Crossblooded archetype it describes how you choose which powers you gain from your two bloodlines it never explicitly states that any of the bloodline class features are altered or replaced. The only thing that is described as being altered is spells known. On Archives of Nethys in the overview of archetypes for sorcerer the only class feature listed as altered or replaced is Spells Known. This may be an error on their part but that’s the source I used when suggesting they would stack.
An ability doesn't have to state that it is altering an ability for the ability to count as altered. Crossblooded is actually involved in an FAQ demonstrating the problem.
https://paizo.com/paizo/faq/v5748nruor1fz#v5748eaic9rai
Sorcerer, Crossblooded and Wildblooded: Can I take both of these archetypes for the same character?
No, because the archetype rules say none of the alternate class features can replace or alter the same class feature from the class as another alternate class feature. Because the crossblooded and wildblooded sorcerer archetypes both alter the bloodline arcana and bloodline powers, they aren't compatible archetypes.Note that it is certainly within the GM's purview to allow this combination. However, the character should not be able to use the crossblooded archetype's ability to select a lower-level bloodline power that was replaced by the wildblooded archetype. For example, a wildblooded brutal (abyssal) sorcerer replaces "strength of the abyss" with "wings of the abyss" at 9th level; the character has "paid" for the wildblooded archetype by giving up "strength of the abyss," and can't use the crossblooded bloodline to select "strength of the abyss" as her 15th-level or 20th-level bloodline power.
It would be nice if AoN updated the Crossblooded overview to reflect this but thems the breaks. Not the only error either. I’ve noticed that the altered class features on the overview of the Agathiel Vigilante archetype doesn’t match the actual text of the archetype at all.
I'm not sure if that's technically an error. The usual text saying that an ability is altered is just reminder text and makes it easier for humans to process. If an ability is changed in some way, then it's altered.
It's probably a super common house rule to ignore these kinds of limitations, and many people will never realize it technically works the way we discussed here. And frankly, allowing these to "stack" will likely not break anyone's game, but I personally wouldn't run the combo unless I knew the GM was cool with that kind of rule bending.
This also reminds me that you probably can't take both blood havoc and crossblooded. You certainly can't replace the bloodline power. And for similar reasons, you probably can't replace a bonus feat that was also altered by the archetype.
And frankly, allowing these to "stack" will likely not break anyone's game, but I personally wouldn't run the combo unless I knew the GM was cool with that kind of rule bending.
Although it has a reputation for being a min-max munchkin archetype thanks to the Orc+Draconic combo, Crossblooded is actually an extremely weak archetype in almost any other situation. Being permissive with it and allowing wild blooded options is unlikely to cause any problems.