Now if the succession was stable for ten generation, father to son or the like, a tradition would be established, maybe even a constitutional convention, which could possibly normalize succession for the next dynasty, providing part of their claim of succession is a claim of kinship and they follow the same tradition for succession. But if there were civil war after civil war of julio-claudian fighting julio claudian, you could have a 200 year dynasty without out creating transition stability. Also more then one or two being assassinated would be bad too. Praetorian Guard choosing which julio-claudian would be bad also.
The best scenario is that it remains mostly within the then existing law, so legitimacy isn't seriously challenged. If you could somehow get Claudius adopted into the Julian line, but then Caligula probably wouldn't of let him live. I've always seen Claudius's accession as the deathrows of the Julio-Claudian dynasty, not because he wasn't a good Emperor, but because he lacked true legitimacy which still needed to be cultivated at that point to further stabilize the monarchy.