Can you improve rings? If so, what's the cost?
Yes, you can improve rings.
The cost is the cost of the highest priced power, plus 1.5 times the cost of all the other powers. It does NOT go up by squares like weapon and armor do.
DMG, p282, sidebar, under "Multiple Different Abilities"
For items that do take up a space on a character’s body (such as a ring or a necklace),
each additional power not only has no discount but instead has a 50%
increase in price.
eg,
Ring of sustenance = 2500gp
Ring of Feather falling = 2200gp
Ring of counterspells = 4000gp
One ring of susenance, feather falling, and counterspells = 4000gp + ( 1.5 x 2500gp) + ( 1.5 x 2200gp) = 11050gp
(Note: the above are market prices. Creation prices are half that)
To improve a ring, you just pay the difference between its final value and its current value.
Edit: also, DMG, p288, last paragraph before the sidebar
If the item is one that occupies a specific place on a character’s
body (see Magic Items on the Body, page 214), 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.