Like the Lyre of Building, Flying Carpets (or Carpets of Flying if you must) are magic items that have the possibility of multiple upgrades that can improve or modify their function. Here are a few ideas:

Speed is the obvious upgrade. The problem for some is that the carpet goes too fast. Over whatever limit the DM wants to impose, the riders have to make DEX checks or reflex saves. Failure results in being swept off the carpet. To prevent this, the creator could put another enchantment on the item, though this will be rather expensive.

Defense not only protects the riders, but the carpet as well. It could be a general force effect that adds Shield to all the riders while the carpet is in flight, a Minor Globe of Invulerability or a Wall of Force that surrounds the carpet (though it prevents outgoing attacks as well). The carpet itself is usually treated as cloth, though with the right magic or alchemical treatments, it could become as strong as mithril.

Offensive upgrades are almost always ranged. A few riders who want a flying ram, but most are more than willing to have a carpet that also acts as a Wand of Magic Missiles, Acid Arrow, Lightning Bolt or Fire Ball. Aiming the effect is part of the command phrase. A few, and obviously expensive, carpets automatically attack as a result of suffering an assault to themselves or their riders.

Cloaking is usually an Improved Invisibility effect that works on the carpet and rider. Occasionally there are versions that also prevent odors and sounds. The latter effect allows the riders to talk to each other, but not to others off the carpet.

Air bubbles can be formed by some carpets and allow the riders to go underwater. With an additional protection against extreme temperatures, such carpets can go into space.

If used to travel at night or underground, a carpet could be upgraded with Dancing Lights, controlled with a command phrase that allows all around lighting. Detection spells that allow all the riders to see the results may also be handy for an upgrade.

A carpet could have one or more sacks sewn into their forms acting as Bags of Holding or a place for Create Food and Water (or other creation type spells). A Portable Hole is also possible but it can only be put on really large carpets and may unfold and open at the wrong time. Dragon 221 has an article on how to expand the uses of a Portable Hole and could help in customizing a Flying Carpet/Flying Fortress.

Speaking of Flying Fortresses, there is also the upgrade that allows more weight. Walls, usually wood or stone, could pop up on command and form a tiny structure. But that would go far over the weight limit of most carpets.

If you want to spend the cash, a Carpet of Flying could become a home away from home.