I've had it explained to me, but not as clearly as I need. Hopefully I can articular the issue clearly enough to get an answer.
Intensified Spell (Metamagic)
Your spells can go beyond several normal limitations.
Benefit: An intensified spell increases the maximum number of damage dice by 5 levels. You must actually have sufficient caster levels to surpass the maximum in order to benefit from this feat. No other variables of the spell are affected, and spells that inflict damage that is not modified by caster level are not affected by this feat.
Level Increase: +1 (an intensified spell uses up a spell slot one level higher than the spell’s actual level.)
So shocking grasp, for example, which caps out it's damage at 10d6 @ level 10, can have its damage dice increased to 15d6.
What about a spell like vampiric touch, which gives you 1d6 per 2 caster levels until 10d6 at CL 20? Does it increase to 15d6, or does it hit a ceiling because the damage scales naturally all the way to CL 20 without intensify?
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It hits the ceiling because the game does not have class support beyond 20th level.
If you could progress to 25th level as an arcane caster than you'd get 12d6 damage for vampiric touch at 24th level.
Untrue. While your CLASS level does not go beyond 20th (Except in homebrew games) your CASTER LEVEL certainly can. A simple core example is Heal, Mass which heals 10 per caster level to multiple targets, to a maximum of 250 (Or 25th CL.)
Orange prism ioun stones are one core way to bump your caster level beyond your character level.
Anyway, back to the OP's question:
1. Shocking Grasp caps out at 5d6 at 5th level, not 10d6. It would be 10d6 at 10th level if you were a 10th level caster with the Intensified Spell metamagic attached to Shocking Grasp.
2. Theoretically, yes, Vampiric Touch would improve beyond 10d6 at 20th, but since Intensified Spell increases the die by an effective five levels, it would only go up to 12d6, because it progresses at 2 die per caster level.
You are correct, I didnt look it up correctly. It's 1d6 per CL until level 5, where it caps at 5d6. Intensify bumps it to 10d6 at CL 10 since you get 1d6 per CL.
Vampiric touch only gives 1d6 per 2 CL, so it's max extra is 2d6, not 5d6,and you'd have to have CL 24, right?
incidentally, your Shocking Grasp example is wrong. SG normally tops at out 5d6, or 10d6 with intensify; rather than 10d6 and 15d6, respectively.
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It hits the ceiling because the game does not have class support beyond 20th level.
If you could progress to 25th level as an arcane caster than you'd get 12d6 damage for vampiric touch at 24th level.
Completely false, as several other people have shown. I do wish more people would look these things up before posting 'em in the Rules Questions forum. There's not a single rule that says Caster Level has a cap in any rulebook.
If you could somehow find a way to bump your CL to CL 30 (ioun stone and karma bead + extra shenanigans that I can't think of), then you could technically have Vampiric Touch do 15d6 damage. But if you only had a way to bump your CL to 24 then yes it would do 12d6 damage.
No, it would cap at 12d6 at 24 CL. It cannot go to 15d6.
The feat adds 5 levels to the advancement. That is level 25. And at CL 25 you do 12d6. This is the cap. Which you reach at 24.