Unless this character happens to have the Death domain, arcane hierophant and mystic theurge are the only classes that advance an arcane class and a divine class simultaneously. Even if he or she does have the Death domain, the class that requires it, the true necromancer, is awful, though it does dual-advance arcane and divine spellcasting (10 levels advance both, 2 levels advance arcane only, 2 levels advance divine only; yes, it is a 14-level class).

However, we can trick our way into a bit more dual-advancement: ultimate magus advances two classes, a spellcaster who prepares arcane spells from a spellbook, and a spellcaster who casts arcane spells spontaneously.

• The wizard prepares and casts arcane spells from a spellbook; that’s no problem.

• The cleric prepares divine spells, obviously, right? Weeeellllll.... they have a class feature literally called “spontaneous casting,” not even the sorcerer does that. And the Alternate Source Spell feat from Dragon vol. 325 lets you use your divine spellcasting for arcane spells and vice versa, so with that feat, the cleric class is casting some arcane spells. And that can include the cure spells they spontaneously cast. So the cleric in this case can spontaneously cast arcane spells. That... is what ultimate magus asks for.

So that gets us in. The wording of the actual spellcasting class feature of the ultimate magus is a little trickier: it specifies that it advances “a spontaneous arcane casting class to which you belonged before adding the prestige class level.” Does cleric now count as a “spontaneous arcane casting class” due to spontaneous casting and Alternate Source Spell?

That question has already come up before: Alternate Source Spell making cleric count as arcane, spontaneous casting making cleric wizard count as spontaneous. In both cases, I go through the problems, specifically that we have zero definition of either of these two terms. In both cases, I recommend against allowing it—but both cases were asking about trying to have a dual-advancement prestige class double-advance a single class. That definitely shouldn’t be allowed. But allowing ultimate magus to advance cleric and wizard? That seems fine to me.

So my recommendation is to allow the player to use ultimate magus here. I would probably not even make them take Alternate Source Spell, though it could be a useful feat for them to have in any case (particularly if they also have Practiced Spellcaster for both cleric and wizard, which they absolutely should).

I can see two reasons why the wizard would not be allowed to change her arcane bond.

Mechanical aspect

The main difference I can see between the fighter / sorcerer example and the wizard is that a familiar provides a constant, specific bonus.

One of the risks would then be that the wizard changes familiar depending on the current focus of the campaign. For example, he would start with an armadillo to protect against attacks, then face more spellcasters and replace it with a dodo for the initiative bonus, later change to a pig because the campaign has more social encounters, and so on.

I always assume that the reason fighters and sorcerers can change their class features is because some feats and spells don't scale well. Wizard bonuses don't scale at all, so this concern doesn't exist.

Flavor aspect

Another difference is in terms of flavor: the wizard is bonded to that item or familiar. Another class that has a bonded companion is the paladin, and while a paladin can change her bonded mount, it takes 30 days during which she has maluses to all her attacks.

On the other hand, there is no connection between a fighter and its feats or a sorcerer and its spells.

Would the game break if the wizard was allowed to change its arcane bond, then?

Probably not. That's, after all, the reason it is included in the retraining rules.

However, other players could get jealous that the wizard gets a flexible bonus that can be changed over time. A ranger might wonder why he can't change his favored enemy, a cavalier might want to change his order, and so on. Those are also bonuses whose utility can change over the course of a campaign.

As for the flavor aspect, it depends on the GM and player. Is a familiar a companion of research and travel, who spends a lot of time with and trusts the wizard, or is it a class feature that provides useful constant bonuses? In the former case, you shouldn't allow the players to throw it away, otherwise they might be torn between the mechanical and the flavor choice.

"I'm sorry, Arthur. We spent a lot of time together and I loved you, but now I really need this +3 bonus to swim more than anything. So, goodbye, old friend."