As written, Multiswift encourages the use of magic items
Here's the thing: The Dungeon Master's Guide on Spell Trigger says, "Activating a spell trigger item is a standard action and does not provoke attacks of opportunity" (213). However, the Rules Compendium on Spell Trigger says, "Activating a spell trigger item takes the same amount of time as the casting time of the spell that the item stores…" (85).
This makes the feat Multiswift an outstanding choice for, for example, a creature that has sufficient ranks in the skill Use Magic Device and a custom magical staff that's been created with spells that have been modified by the feat Quicken Spell (as per DMG 282–3 and expensive but well within the budget of a typical epic adventurer). Of course, the feat will still be useful even without the skill Use Magic Device: many largely mundane adventurers will nonetheless have a spell list or two they can use to activate spell-trigger magic items—assassins, paladins, and rangers all get a pretty big spell lists, for instance—, and, at epic levels, new magic items should be fairly common, and creating new magic items that can be activated as a swift action should be within an epic magic item's creator's power.
That is, the feat Multiswift will see epic yet otherwise largely mundane combatants snapping their fingers to bring forth their magic staffs, buffing themselves or blazing away at enemies with their magic staffs, snapping their fingers again to disappear those staffs, then go about charging their enemies for some of the ol' snicker-snack just like they always have.
While the feat Multiswift does successfully add another limited range of options to the mundane combatant's abilities, the best of those new options are—like pretty much always—just more expensive and ultimately inferior versions of the options opened up by the similar feat for casters, Multispell (Epic Level Handbook 63).
However, if activating magic items is the intended use of the swift action granted by the feat Multiswift—and it very well could be, as that's one way to struggle (quite vainly, really) to bridge the enormous gulf between, for example, epic fighters and epic wizards—, then ignore the next section, and the feat's doing what it should.1
Consider a less sweeping alternative
Having run two campaigns in the past 5 years involving high-powered PCs going from level 1 to level 20 and stopping there, this DM thinks that spending a feat to take every turn an extra swift action is far too inexpensive. Even the feat Multispell feat doesn't go that far, granting, essentially, a swift action that can only be used for casting a spell—a broad and terrifying mandate to be sure, but substantially different from a feat that allows taking a swift action to do anything but cast a spell, like, for example, employ a quickened spell-like ability, use an appropriate Tome of Battle boost, or activate one of those aforementioned magic items.
I think a closer equivalent to a mundane version of the feat Multispell would be a homebrew feat looking something like this completely unplaytested feat:
[Epic] (Fighter bonus feat)
Prerequisite: Base attack bonus +11, proficiency with either two martial weapons, two exotic weapons, or one martial weapon and one exotic weapon.2
Benefit: Once per turn you can take a free action to, at any point during this turn, either take a move action that cannot be used for a normal move or make a standard attack at your full base attack bonus.
Special: You can take this feat multiple times, allowing the feat to be used multiple times per turn. For example, Regdar has the So Fast feat three times. On his turn, Regdar takes a free action to activate the first feat's benefit to make a standard attack. Then he takes a second free action to activate the second feat's benefit to sheathe Dark Edgerazor X, his totally 90s artifact longsword. Then he takes a third free action to activate the third feat's benefit, retrieving from his belt pouch a potion of resurgence. Regdar, despite having done all this, essentially has still his whole turn's worth of normal actions remaining, enabling him—on what is still the same turn—to move 20 ft., drink the potion of resurgence, and activate the benefit of the feat Law Devotion. Regdar's turn is almost as long as Mialee's!
It's this DM's opinion that for the largely mundane folks who plan to spend their combat time primarily hitting monsters with fists, swords, arrows, or whatever that the equivalent to casting more swift-action spells during a turn is not getting more swift actions with which to do whatever they want except cast spells, but, instead, getting more actions to perform the mundane tasks that they wish they always had more time to do yet don't, like stabbing an extra monster, sheathing an artifact longsword, or retrieving a stored item.
1 I totally agree with this answer that it's pretty much impossible keep epic level play balanced—casters really are just that good—, but kudos for considering the martial combatants' concerns.
2 Thanks to this answer for its excellent examination of the original Multiswift feat's prerequisite. Hewing to those recommendations, this feat's prerequisite isn't met automatically by the typical human epic cleric, druid, wizard, or sorcerer yet is met automatically by any other core rules standard class; unfortunately, some nonhuman full casters will be able to meet them, too.