Was the American Civil War the first to include multiple multi-day battles?

The Civil War is considered the first "modern" war for many reasons, one of which is that it is the first example of trench warfare. It was used in the Siege of Petersburg, which is not actually a "siege" but a series of nine offensives, seven of which were multi-day battles over an 11 month period. The Union won at the Battle of Fort Stedman and those battles are also offensives that run directly into each other. (The OP asks for examples of wars with more than 4 multi-day battles or 3 in one year, but this is far too generous). The Western Theater included 6 multi-day battles. The Army of the Shenandoah fought a multiday battle at Battle of Fisher's Hill. The Gettysburg Campaign included 4 multiday battles. (This is not a comprehensive list).

The number of multiday battles in the Civil War WAS indeed unusual and would become a hallmark of conventional warfare that followed it.

There were several advances in weaponry made during the war, including the Gatling Gun. It often wasn't well employed in early battles, since modern artillery strategy was new, but it contributed the most to the high number of multi-day battles by leading to the development of trench warfare. Smalls arms also become much more deadly at this time due to the development of repeating rifles and the mine ball. The land mine was also used in the American Civil War. Deadlier weaponry combined with the South having a smaller army caused them to develop a defensive military strategy which lengthened the time of the military engagement.

The main criterion for having multi day battles is having an army left after an initial engagement. In the Civil War generals often defended against assaults and then remained stationary or only drove off their opponents until they reached there own defensive positions. To take the first and second days of Gettysburg as an exapmple : The confederates attacked, were repulsed but were able to reform their lines and such fight on the next day. The devellopment of the minie ball and artillery made defending much easyer then attacking. Why did ancient battles never last longer then a day (and often not much longer then a few hours) is mostly because when the infantry would dissengage (like for example Hood's men at the peach orchard) they would be immediatly run down by heavy cavalry and routed. The Civil War saw very little routs compared to other wars.

Both parties always got away with a large part of their force. This caused the war to drag on this long. The goal of the generals on both sides was to 'destroy' the enemy,which they failed at on both sides.

Lastly there is the following to take into account. Pitched battles. The civil war saw no pitched battles, they were always engagements by maneuver, of one side trying to achieve a strategic objective. But in old times there often simply was this : two armies would march toward another to a field, encamp for the night and fight it out at first light. They would engage not always on the best ground (In the english civil war there is a battle where on side actually came down from the high ground so that the other side would fight) In these scenario's of 'all or nothing' with things like schivalry involved, chances are that one army will simply run for their lives if the assault fails.

The Battle of Gergovia and Battle of Alesia were both multi-day battles in the Gallic revolt of 52 BC. Being two battles in the same war, both ending on a different day than they began, that seems to qualify as multiple (ie more than 1) multi-day (ie lasting through more than one single midnight-to-midnight time period) battles.

Also the Battle of Leipzig, October 16-19, 1813, was fought over four days, longer than any (non-siege) battles that I know of in the American Civil War.

I don't know enough about other wars to know if the American Civil War featured more multi-day battles, but will take a stab at why it did, and why others might not.

The North and South had very different advantages. The North had a numerical advantage that ran has high as 2 to 1 in the latter part, while the South had the better generals. Thus,

There were several American civil war battles where one side, typically the South got the better of the other the first day, and then the second side, the North, got the better of it on the second and subsequent days. That would be because a skillful southern general caught "half" (or so), of a Union army at a numerical disadvantage on the first day, while the North received reinforcments that turned the tide on the second day.

At the battle of Shiloh, for instance, Confederate general Albert Sydney Johnston attacked Ulysses S. Grant with 47,000 men against 33,000 for Grant. The South was winning until Johnston was shot and killed, which may have put a damper on Southern morale. Also, Grant had assembled ALL of his artillery (field artillery, siege guns, gunboats) at the Pittsburgh Landing for a "last stand" (the Union had an important advantage in this branch of service.)

Grant received reinforcements of 28,000 on the second day, his own "lost" division under General Lew Wallace (future author of Ben Hur) and three divisions of a supporting army under Don Carlos Buell, and won the battle the second day.

At the battle of Gettysburg, the Confederate infantry got much the better of it the first day against one third of the Union army, but the remaining two thirds arrived the second day and held off the Confederate attacks. On the third day, the Confederates received the belated arrival of their cavalry, which helped bolster their spirits enough to launch "Pickett's charge," and the rest is history.

What these battles had in common was a temporary Confederate advantage in the early part of the battle, and a decision in favor of the Union when they received reinforcements on the second day.

Why didn't this happen in other battles of say Marlborough? In most cases, the two sides were more evenly matched inb both numbers and generalship, and there wasn't a pattern of shifting fortunes due to the presence or absence of half or so of one side's army. The multiday battle pattern appears NOT to have anything to do with American exceptionalism.

As for the ancient multiday battles, Thermopylae was basically a siege, at least after a Greek traitor showed the Persians a "back" road over which to surround the Greeks, while the battle of Leipzig was decided by some Saxon troops deserting Napoleon and joining the Allies, reinforcing them, and "de reinforcing" Napoleon.