No rules prevent adding new abilities to—or improving existing abilities of—potions, scrolls, and wands
The rules on Adding New Abilities discusses magic items generally and only makes an exception for the weary GM to say no in the case of magic staves ("Because staff pricing is so complex, a GM might want to forbid adding new abilities to staves…"). Thus, so far as I'm aware, you've missed nothing, and a potion, scroll, or wand can be improved after its creation… so long as the standard rules for creating the item are adhered to, of course.
With that in mind, on Adding New Abilities, in part, also says, "If the item’s current and proposed abilities follow the normal pricing rules…, adding the new abilities is a matter of subtracting the old price from the new price and determining how many days of crafting it takes to make up the difference." There's more to this, of course (e.g. acquiring raw materials, finding an appropriate locale, meeting prerequisites necessary to to add the ability to the item, staying within the bounds of the magic item involved—just because it's already a wand of fireball (3rd-level spell at caster level 5) doesn't mean the spell level of a wand can be exceeded by adding to it the feat Maximize Spell, for instance!), but, in the end, it seems these same rules should apply equally to potions, scrolls, and wands.
While this GM hasn't, like, built a campaign around this idea, he has allowed PCs to upgrade all three of potions, scrolls, and wands: the first two when it was convenient to have a particular spell in a potion or scroll be a higher caster level (I think it was the water breathing spell), and the third when the rogue had some spare cash to spend on her backup wand of magic missile (1st-level spell at caster level 1) so as to improve it to a wand of magic missile (1st-level spell at caster level 3). My campaigns didn't explode. However, I've only had limited experience with PCs doing this, and no player has sought to take these ideas to extremes. In other words, it seems fine in small doses.
The risk of super serums
I think there's some risk to the campaign when new abilities are added to potions. That's because I suspect that most folks' expectations would be that when a potion is consumed, all of the potion's spells immediately take effect.
This isn't a big deal when discussing a a potion of cure light wounds, cure light wounds, and cure light wounds (each a 1st-level spell at caster level 1) (50 + (2 × (50 + 50%)) = 200 gp; 0.1 lbs.) that heals 3d8+3 points and obsoletes in all but weird edge cases both the typical potion of cure moderate wounds (300 gp; 0.1 lbs.) that heals 2d8+3 points of damage and is a strong contender to obsolete the potion of cure serious wounds (750 gp; 0.1 lbs.) that heals 3d8+5 points of damage. Who cares? Healing's usually easier and cheaper with wands anyway.
This becomes a big deal when discussing a potion of invisibility and fly (2nd-level spell at caster level 3 and 3rd-level spell at caster level 5, respectively) ((300 + 50%) + 750 = 1,200 gp; 0.1 lbs.) that grants the consumer the effects of both the invisibility spell and the fly spell. Allowing a creature to take a standard action—or a move action even!—to get the effects of several buffs strains an already fragile action economy. (And—wow!—will players will quickly grow to hate that potion!)
Although benefiting from a potion takes a standard action that provokes attacks of opportunity, that's all it takes, and the presence of these super serums could radically alter the campaign. For instance, a lone potion that grants its consumer a baker's dozen 1st-level buffs is just 950 gp. During low- and mid-level encounters, keeping the super serum out of the enemy's belly may become a bigger priority than even taking out the finger-wiggler over there in the pointy hat.