I have previously talked about the nominal issue of weapons to U.S. infantrymen per the table of organization and equipment here. A certain reasoning was used in the table of equipment issue of weapons to each man depending upon his position. For example, the platoon commander was directly on the front lines and was expected to be able to defend himself properly, but he was not expected to partake directly in firefights, which would mean he would be neglecting in the maneuvering of his squads. Instead of an M1911 pistol (usually issued to officers in rear areas) or an M1 Garand (issued to his riflemen), he was given an M1 carbine. Once a unit entered combat, however, some portion of the theory and what was supposed to happen in combat per field manuals and tables of organization and equipment was chucked right out the window, replaced by whatever would complete the mission in the most efficient manner, cause the most death and destruction to the enemy, and keep friendly troops alive.

One example of a high-level improvisation would be Change 1 to T/O&E 7-17 (infantry rifle company), first promulgated on 30 June 1944. In the hedgerows, it was common that every one in four or so Germans (or even a higher proportion) would have some type of fully-automatic weapon, be it a submachine gun or a full-power machine gun. Six M3 submachine guns (useful for close quarters urban combat or patrols, or "special missions" such as bringing back prisoners for questioning) and six Browning Automatic Rifles (enough rifles to give two thirds of the squads in the company a second one) were added as a special weapons pool in the company headquarters, to be issued as the company commander saw fit.

Other improvisations weren't by the book. The systematic issue of a second BAR to all rifle squads on an unofficial basis predates this regulation; the 164th Infantry Regiment of the Americal Division was doing it on Bougainville as early as the end of January 1944:

Contrary to the official Table of Equipment, each squad now had two Browning Automatic Rifles for additional firepower.

This arrangement was also used on Kwajalein, Saipan, Leyte, and Okinawa by other Army units:

The rifle units now use two BARs per squad. They used it for Saipan, Leyte, and Kwajalein, as well as Okinawa, and find them especially good for night defense. They would like them in the T/E.

Company M of the 134th Infantry Regiment learned from the 116th Infantry Regiment, whom it was relieving, about operating heavy weapons in Normandy hedgerows:

During these attacks, Company M's machine gun platoons had been attached to the assault companies. The heavy machine gun were being mounted on light machine gun tripods or on improvised bipods, or with no mounts at all, were fired by laying them on the tops of the hedgerows. By this time, however, the heavy weapons company had become practically a "light" automatic weapons company. Through battle-field recovery, salvage, repairing, and shrewd trading in the rear areas (of enemy pistols or machine guns for U.S. automatic rifles), executive officer Virgil Hyde had been able to replace most of the heavies with light machine guns or with BARs--a popular favorite in the hedgerows; and he had added a few Thompson submachine guns for good measure.

After the Battle of the Bulge, the systematic issue of two Browning Automatic Rifles per squad became common in the European Theater:

Wed 17 Jan 45 -- Today two Browning Automatic Rifles (BAR's) were authorized for each rifle squad; the additional fire power should help.

....

I was carrying a BAR. We had beefed up our firepower with two BARs to a squad...

"Dual wielding" of weapons (i.e., a rifle and a submachine gun), far from a video game trope, also occurred (see 3:10). The 399th Infantry Regiment daily S-4 (supply) report for 15 December 1944 states:

"Drew from 800th Ordnance Fifty-two (52) Gun Mach Cal 45 M3 on special authorization of Seventh Army for purpose of line companies, Battalion Headquarters and MP Platoon to increase firepower. Two (2) more of same weapons still due in to complete requisition."

This total brought the number of submachine guns in the regiment to 115, nearly as many as the number of Browning Automatic Rifles authorized.

Sources:

Bellanger, Yves. U.S. Army Infantry Divisions 1943-45, Volume 1: Organization, Doctrine, Equipment. Solihull: Helion and Company, 2008.

Cooper, Jerry, and Glenn Smith. Citizens as Soldiers: A History of the North Dakota National Guard. Lincoln: University of Nebraska Press, 2005.

Huston, James A. Biography of a Battalion: The Life and Times of an Infantry Battalion in Europe. Mechanicsburg: Stackpole Books, 2002.

Leinbaugh, Harold P., and John D. Campbell The Men of Company K: The Autobiography of a World War II Rifle Company. New York City: William Morrow and Company, 1985.

Krehbiel, Bill J. The Pride of Willing and Able: A Chronology of Company L, Third Battalion, 319th Infantry, 80th Division in World War II. (Independently published, 1992).