Multi-Armed Multitasking

You look in the mirror and see three heads looking back at yourselves with five eyes and seven arms and think to yourselves, how do we septo-wield? Or better yet, how can we write our book, cradle our baby, and make paper airplanes at the same time? Practice, that's how.

Please note this has surprisingly little to do with Excuse Me While I Multitask, if you're thinking about wielding weapons with many arms you still need some form of Multi-Armed Multitasking; it just belongs in Multi-Armed and Dangerous. If your extra limbs are for walking, they belong in Spider Limbs.

If a character has extra arms but doesn't uses them to do two (or more) things at the same time, that's "just" Multi-Armed and Dangerous, which is a supertrope to this trope.

Examples of Multi-Armed Multitasking include:

Anime and Manga

In Squid Girl, Ika has this with her tentacle hair.
Spirited Away - Kamaji operates the bathhouse boiler room. He has six spidery arms, which he uses to multitask: reaching into the hundreds of herb cabinets, pouring boiling water, grinding potions with his yagen (related to a mortar a pestle, but using a wheel in a narrow trough) and responding to wooden tags on ropes signalling requests from the bathhouse above.
Franken Fran oftentimes attaches her head to a special multi-armed body in order to perform particularly complex surgery.

Comic Books

In Ironwood, first mate Tif makes full use of all four of her hands while having a threesome with a jinn and a crewmate.
Spider-Man's foe Doctor Octopus. According to The Official Handbook of the Marvel Universe, he can use his regular hands with his four mechanical tentacles to preform one complex task and two simple tasks simultaneously, and as some stories show, the "complex task" can even be a heated battle. He has been known to do things like casually light a cigarette while his tentacles fend off attacks from multiple enemies.

Fan Works

There was once a Mortal Kombat fan fic where Sheeva was driving somewhere with the heroes, and had two arms on the wheel, one on the transmission, and one out the window (and no, it doesn't mention how she learned to drive).

Film

The bar-tending octopus cartoon from Who Framed Roger Rabbit?.
- Similarly there's a sushi chef in Monsters, Inc..
- And the guy in the octopus costume from The Princess and the Frog.
The twin Mission Controls from Men in Black.
- the mail-sorting alien in MIB 2.
Long John Silver in Treasure Planet isn't multiarmed but still manages to pull off this trope in the kitchen, thanks to his multi-purpose cybernetic arm with little armlets.
From Spider-Man 2, Dr. Octopus does this when he built the new sun-generator machine, with his long metallic tentacles.
Star Wars featured a restaurant run by a chef with four arms.
At one point in Terminator 2 the Voluntary Shapeshifter T-1000 grows a third arm to pilot a helicopter and load a machine gun at the same time.

Literature

In The Hitchhiker's Guide to the Galaxy, Arthur's extreme Unknown Rival Agrajag has built a Temple of Hate devoted to him, the centrepiece of which is a giant statue of Arthur with multiple arms. He discovers that each one of them depicts one of the many, many times he has (unwittingly) caused the death of one of Agrajag's former incarnations.
- Subverted with Zaphod Beeblebrox, who gave himself a third arm and then does nothing at all with it.

Live-Action TV

Pilot from Farscape. One episode notes that having the mental capacity for multitasking is very uncommon, and more important than the multiple arms themselves.
The short-lived 1970s sci-fi sitcom Quark featured Interface, a four-armed alien woman who worked as an intergalactic switchboard operator connecting calls between ships.
Kamen Rider Fourze has the Hand Switch, which equips Fourze with an extra arm (attached to his leg) that's outright stated to be for this. While he works on solving a math problem, it disassembles a bicycle. Thus far its not been shown to have any type of combat potential.

Mythology

Hindu Mythology several gods (Shiva for one) are usually depicted with multiple arms each holding symbolic instruments like scales and scythes and swords.
Different Buddhas are sometimes depicted with many arms.

Tabletop Games

GURPS has the Multiple Arms advantage available for player characters, but you also need to buy special coordination to use them fully- otherwise they are only good for holding things, not performing more than one task at a time.
In Werewolf: The Apocalypse, the Ananasi werespiders can take this ability, though it's a fairly high-level spell, since it requires a fair deal of mental skill.
Techpriests in the Warhammer 40,000 universe can do that.

Web Comics

Schlock Mercenary had it played with in several ways. Andy is a Fobott'r (generally humanoid, but four-armed species) During his initial interview, he bragged about quad-wielding handguns, but Thurl just pointed out that he still only had two eyes, so no matter how many weapons he's got, he'll only hit one target. There has been incidents where he has used it, though - including wielding a two-handed assault-rifle and two handguns at the same time - but it's been purely for intimidation-value. Or sometimes just for fun. It's still useful in having extra free hands for tasks not requiring sight, e.g. they can hold and use a weapon or two with one pair of hands, and get something else ready at the same time. And specifically Fobott'r have an option of using one hand to read their Tactile Script.
- Schlock himself has demonstrated on multiple occasions that he can not only form extra hands when needed, but also use them quite effectively. The fact that he can have multiple eyes (if he can get hold of them) means he could aim at multiple targets.

Western Animation

Elzar in Futurama. The DVD commentary mentions that the animators went out of their way to have each arm work independently rather than have each arm on either side move in the same way.
SpongeBob does this taking care of the baby scallop, probably other times as well.
Squiddly Diddly did this sometimes. (In fact his pic on The Other Wiki shows him playing three musical instruments at once.)
In The Simpsons, a cutaway shot of the Earth shows a vaguely Hindu-esque being frantically pressing buttons in the core, apparently to keep the world working. He pauses briefly to wipe his forehead with one of his hands and sigh with exhaustion.
One episode of Dragon Tales featured a dragon with six limbs running a concession stand.
In an episode of Arthur, the titular character has to clean a room, and his dad tells him "Many hands make light work." He imagines it literally. Buster does the same later in the episode.
Spydra in Gadget Boy and Heather does this at times in a few episodes, making full use of her six arms simultaneously.
In the cancelled series Stripperella, a supervillainess with six arms pilots a blimp all on her own, with two hands on the wheel and the remaining four on switches and buttons. She also utilised six pistols at one go in the earlier portion of the episode, allowing her to use them as a makeshift machine gun.
Ceres from Oban Star Racers, an Animesque racing series co-produced by French and Japanese animation studios.