Mostly for weapons and armor. For instance, could create a Flame Tongue with a bonus higher than +1, or boost it over +1 after the initial creation/purchase? How would calculate the cost?
Same goes for more complicated weapons, like a Sun Blade for instance. Could you further upgrade it? How would it interact with the fact that the weapon enhancement bonus is variable depending on the situation?
What about stats item? Could you boost your +2 Headband of Vast Intelligence into a +6 one?
(I'm starting with the assumption that you can even upgrade a magic item at all, by covering the difference in cost between the upgraded and original version, like it seems to be the concensus. Also, I believe Joshua Frost has posted something about this, but I think he meant the cost in PFS watchamacallit points).
Adding New Abilities
Sometimes, lack of funds or time make it impossible for a magic item crafter to create the desired item from scratch. Fortunately, it is possible to enhance or build upon an existing magic item. Only time, gold, and the various prerequisites required of the new ability to be added to the magic item restrict the type of additional powers one can place.
The cost to add additional abilities to an item is the same as if the item was not magical, less the value of the original item. Thus, a +1 longsword can be made into a +2 vorpal longsword, with the cost to create it being equal to that of a +2 vorpal sword minus the cost of a +1 longsword.
If the item is one that occupies a specific place on a character's body, the cost of adding any additional ability to that item increases by 50%. For example, if a character adds the power to confer invisibility to her ring of protection +2, the cost of adding this ability is the same as for creating a ring of invisibility multiplied by 1.5.
Yes, you can upgrade items, making a +2 headband a +6 headband, you just need the correct feats and gold equal to the difference in the crafting cost of the 2 items.
Upgrading special weapons and armor, by the RAW, no. By the RAW a +2 version of a flame tongue weapon does not exist, thus there is no way to know what the material cost.
You can reverse engineer the cost of a flame tongue and make house rules for upgrading it.
I'm starting with the assumption that you can even upgrade a magic item at all, by covering the difference in cost between the upgraded and original version...
The answer is yes and maybe.
'Yes' you can absolutely upgrade existing armor and weapons and items by paying the appropriate cost difference and finding an appropriate crafter/caster to do so. Rules for this are covered in the core rules and in additional detail in the Magic Item Compendium from 3.5, if you use that material.
'Maybe' is in regards to specific magic items like Flametongues, Sunblades or Mithril Full Plate of Speed and others like them listed in the rules. Fluff says specific items are the result of magic processes and forumla that end up making that specific item in that specific power.
Some GM's rule that tampering with them after the fact disrupts the 'magical balance' that makes them what they are and so do not allow it.
Some are happy to attempt to reverse engineer the items using the known powers and making judgement calls on pricing for the unique properties of those that have them.
Your DM will probably have the final verdict.
Personally in our games we allow modification of anything but the ref is careful to monitor what gets made and how to make sure balance is kept in mind.
Edit: Charender with the ninja speed.
There's no RAW for upgrading a specific weapon. Here are two house rules you can consider:
Generous Upgrade (probably not recommended): Any features other than the enhancement bonus are calculated as straight +gp features. The Flame Tongue is a +3 equivalent weapon with an extra +2400 gp from the touch attack feature, so upgrading it is the same as upgrading a +3 equivalent weapon. A Flame Tongue with a +2 bonus instead of a +1 would cost 34,715 gp (+4 longsword plus 2400 gp). A Sun Blade with a +3 bonus instead of a +2 would cost 60,335 gp (+3 bastard sword plus 44,000 gp).
Stingy Upgrade (what I'd recommend): Calculate the entire base price of the weapon as an equivalent enhancement bonus, then add one to that bonus to determine the upgraded price. The Flame Tongue is a 3.2 equivalent weapon; adding another +1 will increase its price to 35,490 gp (price for a +4.2 longsword). The Sun Blade is a +5 equivalent weapon; adding another +1 will increase its price to 72,335 (price for a +6 bastard sword).
Assuming the weapon was fairly-priced to begin with, whatever method you choose should probably result in a price somewhere within this range.