Rasputin, how are level 14 players supposed to deal with this? Major spoilers.

Simply put if everything goes wrong suddenly the encounter vs. Rasputin is against Rasputin, 3 vampire anti-paladins, one daemon, and five advanced shadow demons. A total of 203,200 xp, just 1600 short of a cr 19 encounter, and one that is quite strong for it's level.

You have a full caster that is fully buffed, can cast miracle 3 times, and needs to be killed 3 times before he dies (an attribute not reflected in his CR I might add) 3 melee with fantastic attack and damage and defense againt good, and ridiculous regeneration with both fast healing and touch of corruption as a swift. Not to mention more than 160 hp base each. The daemon can control to an extent and helps Rasputin by complimenting his powers. 5 advanced shadow demons, well low cr, but they target touch AC, and are incorporeal meaning they probably are taking half damage from attacks. And they know all the PC's weaknesses and have told those to Rasputin.

Rasputin will be hard enough on his own, what do I do to help the PC's survive a APL+5 encounter if everything just doesn't go their way?

I think it is more accurate to say that they face off against all the other opponents first before they face Rasputin.

But if you want to be creative you can have the players gain mythic tiers over the course of the adventure (adding tiers to opponents when applicable).

In this senerio, Rasputin is busy absorbing mythic power from Baba Yaga to fight the heroes at that point so the heroes can fight all of the non-mythic villains first in order to clear the room, then have Rasputin pause from his work (have his mythic tier be equal or one level higher then the heroes) to fight the heroes.

But all those enemies have conditions under which they flee to join Rasputin, especially the shadow demons. Giving the heroes mythic, and giving Rasputin mythic would keep things status quo, a CR 19 encounter vs lvl 14 PCs. Rasputin is not an idiot, he will fight the pc's with the minions, it's implied that that is what he is supposed to do. It's stated that they fight -with- him. Aside from changing the tactics of the enemies how do I make the encounter survivable. I mean I could just rule Rasputin never casts a spell higher than level 4, but that does not make much sense.

I'm considering divine intervention, giving them the equivalent of full rest and spells right before the encounter and maybe some planar allies. It's just that that isn't really in tune with the jive of the adventure.

If you feel that it may be too much, perhaps alter the tactics of Rasputin's allies so that they don't flee to his side. Have them fight to the death to stop you from getting to Rasputin instead, or when one of them goes back to warn the mad monk, he orders them back into the fray. Something like that.

If every single one of those enemies manages to get away from your PCs and join Rasputin, your players have screwed up very badly.

If the PCs botch that badly, the most I'd do is strongly hint that the players need to withdraw and come up with a plan.

Their best bet would probably be to engage Rasputin and then pull back in such a way that the Brothers Three, etc. pursue them and re-engage separate from Rasputin.

Rasputin won't leave the World Engine, but he may order his servants to pursue to finish the party off.

Hmmm. Sudden allies that might actually fit... My suggestion for that would be fey. Specifically, fey from the Thrice-Tenth Kingdom that have noticed what Rasputin is doing, and don't really want him as their new lord. Just what those are fey are could be whatever you feel like, though they shouldn't be good-aligned.

Hmm, k I'll think about this.

You could even throw in temporary allies for this adventure like a Russian gunslinger who is a veteran of the Russian army captured by rasputins forces. This character can also be the individual who returns to st.petersburg to spread the rumor that Anastasia is alive.