Were there ever wars/battles where infantry were given multiple rifles to speed up rate of fire?

It was common in the age of single shot muzzle loading muskets and rifles for people to load guns and pass them to the shooters, especially when the defenders were civilians. Thus I read of a Texas family successfully defending against a hostile Indian attack where everyone in the family loaded the guns and passed them to the 12 year old boy in the family who did the shooting.

According to Wikipedia at the Battle of Coleto March 19-20, 1836:

Each Texian soldier received three to four muskets.

https://en.wikipedia.org/wiki/Battle_of_Coleto1

I assume that the Texians preloaded their muskets before the battle and during every lull.

No doubt detailed accounts of the battle explain exactly how the Texians used their multiple muskets.

You are describing something similar to the mitrailleuse gun, which had several manually-loaded barrels. It may not have been used by infantry, but seems to meet your other criteria.

I've read that this was done in The Battle of Blood River and it seems to be suggested by the account on wikipedia as well.

The practice of having men re-loading guns under cover and passing them to someone else to fire must have happened many times. Sensible soldiers would do it whenever it looked like a good idea. This is most likely when there are a few good positions to fire from, and anyone trying to shoot from elsewhere is unduly exposed to the enemy.

The Ross Rifle's unreliability under trench warfare conditions gave rise to a variation of this practice. It was very prone to jamming when dirty, so it made sense for several men to work on getting rifles ready to fire and pass them to one man in position to shoot. A contemporary account records it being necessary at times to have five men working to keep one rifle firing.

In Medieval times, with crossbows, yes-- crossbow teams were used both in attack and defense.

Crossbowmen among the Flemish citizens, in the army of Richard Lionheart, and others, could have up to two servants, two crossbows and a pavise to protect the men. Then one of the servants had the task of reloading the weapons, while the second subordinate would carry and hold the pavise (the archer himself also wore protective armor). Such a three-man team could shoot eight shots per minute, compared to a single crossbowman's three shots per minute. The archer was the leader of the team, the one who owned the equipment, and the one who received payment for their services.

*Verbruggen, J.F (1997). The Art of Warfare in Western Europe during the Middle Ages, second revised and enlarged edition (English translation). Boydell&Brewer. ISBN 0-85115-570-7.

I speculate that in more modern (Colonial, Napoleanic, etc.) times, it was far more efficient to have multiple rows of riflemen working in tandem. It also better fit the economic model of the times, where you had a group of soldiers, not 2-3 servants to a soldier. Also it's a more robust method, since if the shooter is taken out in the crossbow team, it can no longer fire effectively.

I'm not aware of such tactics for infantry, but having several pre-loaded weapons was fairly common for cavalry units. For example, cuirassiers typically carried two loaded pistols. They would discharge the 1st pistol from close distance when approaching the enemy at speed, right after that they would pull the sword for the hand-to-hand combat, and if they had to retreat they would shoot the 2nd pistol backwards. They certainly didn't have time to reload during the sword combat between the shots.

It seems a defending force could have benefited from having extra, preloaded weapons available (particularly before weapon reloads got fast enough to make it less of an issue).

As a planned tactic, this is impractical with longarms for an entire unit; it's too expensive to equip a unit with extra guns, and it's too heavy to lug them around. Being able to fire two or three shots in fairly rapid succession is not a great advantage with guns as inaccurate as a smoothbore musket, soldiers who aren't trained to aim, and battles that can last hours. Once you've fired off your prepared shots, now you're back to hand loading for the rest of the battle. Better off using that money buying better guns.

What you might have is two people with two guns. One fires the gun, then they pass it back to be reloaded while being handed the other loaded gun. But this was pretty uncommon. It was more a tactic used when you had soldiers defending civilians, might as well put them to use. Unfortunately I don't have a historical example of this, it could be something Hollywood made up.

What you might also have is a prepared defense which finds themselves with too many guns and not enough soldiers. In this case, circumstance might lead them to assign several loaded guns to each soldier, perhaps to their best soldiers. Again, I don't have an example of this.

Instead, the effective fire was increased with volley fire. It's depicted wonderfully in this scene from the movie Zulu. The infantry is broken up into two or more ranks. One fires while the other reloads. The result is a continuous volume of fire, there's no lull in which the enemy might charge at you. This required an immense amount of training both in rapid reloading, and the volley fire drill.

Keep in mind that warfare at this stage is largely about morale, convincing a group of people to willingly walk into the line of fire, using guns with an effective range of about 50 meters. Aiming was optional.

In fact, when multi-shot magazines were introduced militaries insisted they have a "magazine cut off" which prevented the gun from using the bullets in the magazine; they had to single load. The idea was to conserve ammunition by firing single shots. The magazine was held in reserve to repel a charge. Needless to say, this idea was quickly dropped once experience was gained with rapid fire (by "rapid fire" I mean a bolt action rifle).

Where it was done was with single-shot pistols. The picture of a boarding party going into battle with two or more pistols on their belt was real. It made sense in a brutal, short, close range battle: fire it, drop it, draw a new pistol. It also dealt with any reliability issues, if the pistol doesn't fire, drop it and draw another one.

There's also multi-barreled weapons like a double (and triple!) barrelled shotgun. This is, essentially, multiple loaded chambers with multiple barrels sharing a common stock. This allows you a quick follow up shot, but also a diversity of shot. A hunter might have birdshot in one barrel, buckshot in another. But militaries didn't use them because battles last longer than two shots, and you're back to reloading.

This evolved into the revolver, which is essentially multiple loaded chambers with a single barrel. An early example is this Puckle Gun, an example of a manually indexed, black powder, muzzle loading revolver. Now you have five, six, or seven shots before you need to reload providing a sufficient advantage for militaries to take interest, at least for pistols. But a revolving rifle has fundamental design issues, namely gas leaking between the chamber and the barrel, "cylinder gap", limiting how powerful a powder load you can use in a revolver of the period.

Magazines would not become popular until the end of the 19th century.