We don't discuss this period enough, I feel. So:
The marriage of Augustus' daughter Julia to his stepson Tiberius in 12BC quickly soured, which may in large part have been down to the death of their only daughter, who was either stillborn or died in infancy: I forget which. Anyway, what if this daughter is born a boy, and then survives and prospers, allowing Tiberius and Julia's marriage to continue. Julia remains a permanent fixture on the Roman scene, and may deliver Tiberius more children, although for simplicity's sake let's assume that either they're daughters and/or they die young.
So, that's all well and good. Now, though, let us assume that Gaius Caesar, Julia's son by Agrippa who had been adopted by Augustus as a boy, also survives after suffering his wound in Armenia in 4AD. Gaius' personality, from the scraps we know, seems to have suffered somewhat due to his being spoilt by Augustus as a teenager, so by Augustus' death, which we'll see is postponed by a year to AD15 due to a less stressful succession-hunt, he'll be something of an arrogant thirty five year old.
Augustus now has three potential heirs: an experienced general in the form of Tiberius, and not one, but two adult grandsons (probably with children of their own at this point) in Gaius Caesar and Tiberius' son who I'll call Julius Claudius Nero. How do things play out from here?