What follows might be a tangent, so I apologize in advance.
US Army doctrine and organization and Canadian doctrine and organization are similar but, of course, different. I took my "Captain" training with the US Army, and I'll try and hit on the big differences. I trained under the four company construct, but I'll try and put it in a three company construct here.
An armor battalion would have three tank companies with 14 tanks each, plus two in the Bn HQ. It would belong to a Brigade that in turn would belong to a Division. A Brigade might have one armor and two infantry battalions or vice versa. Normally, battalions would swap companies and then become "Task Forces." The armor battalion Task Force might then have two tank companies and one infantry company (mounted on Bradleys). As as aside, both armor and infantry battalions had their own Scout platoon and mortar platoon.
That battalion Task Force CO might choose to keep his companies "pure", or he could cross-attach some to form two company teams and one "pure" company. You might then have one "tank-heavy" company team (two tank platoons and one infantry platoon), one "infantry-heavy" team (two infantry platoons and one tank platoon) and one "pure" tank company (three platoons). With the four company construct it was easier to swap two companies each and form Teams throughout.
The company teams or companies would usually operate together, although terrain would dictate. The CO and S3 would usually be forward in their tank or Bradley. In terms of tactics, a company team could attack a platoon on its own, or it might be a battalion operation. It could mean that a infantry-heavy team would assault an enemy platoon in "wedge" formation, with the tank platoon leading and the two infantry platoon trailing slightly. The tanks push through or around the trenches, while the infantry clear them out. Another company might be providing a "support by fire" position and another might have been given the task of breaching any tactical obstacles. Regarding enablers, we didn't plan on AH-64s and A-10s. Those were assumed to be focused on the Divisional Deep Battle. Mortars and artillery were the expected fire support.
In Canadian doctrine, we had a brigade group with (in theory) three infantry battalions and one armoured regiment among other things. This brigade group is thus larger than the "standard" US brigade. In practice, however, the Canadian brigade group had two infantry battalions and one armoured regiment. This reveals the start of the problem of analysis. I found that the US taught and trained with formations that existed in reality. In Canada we usually have a vast gulf between theory and practice.
Assuming for laughs that the CMBG had three and one, groupings could be varied. You might see all three tank squadrons pulled away and attached to infantry battalions, leaving the armoured regiment CO all alone. You might see two squadrons given out but get one or two infantry companies in return. In the two battalion/one armoured regiment construct you could see two infantry heavy battlegroups and an armoured regiment with a single squadron and perhaps a company.
Going down to Battle groups, an infantry CO might split his squadron up to the companies, giving one troop to each company. Alternatively, he could form a single "combat team"and have two infantry companies on their own.
Our square combat teams were big affairs. A complete squadron with a complete company, almost a mini-battalion on its own. Since a battalion could often only form one of these, this didn't leave much for the CO to manoeuvre. You could then see half-squadron doled out to two infantry companies, giving two combat teams.
Many of our combat team attacks would be battalion attacks if conducted by the US given the same resources. Where we would have a combat team they would have two company teams under the CO or S3.
In Canada we focused on the lower-level. Big battle groups and big brigade groups. That makes a certain amount of sense for us. The US Army seemed focused on the Division. Everything under the Division was arranged to support Divisional operations, pointe finale. As the US shifts focus to Brigade level, we might see a change in organizations and doctrine. Who knows. Our brigade group may have been ahead of its time. Resourced properly, its a great formation. I beleive, however, that we are an Army with its heart at the Combat Team level. Not necessarily a bad thing these days, given how operations are conducted!
I found during training (at the schools and the field force) that we didn't seem to worry about higher-level implications. Even on brigade exercises we often only had one combat team "up", since there were rarely many tank squadrons. On the many JANUS exercises where we did try to play big picture, we solved the problem by adding sub-units (magic). A battle group could suddenly end up with three or four square combat teams, and the brigade might have two such battle groups. Great fantasy that bore little relation to reality ("I never thought it would happen to me...")
When COs and Brigade Commanders "played it real", we sometimes saw single troops attached to companies and SHQ conducting a two-tank firebase. We also saw commanders taking the squadron size down to three troops when they found that be borrowing a few tanks from elsewhere in the army they could get two tank sub-units. I think that that was the genesis of the three-troop squadron.
I think that we often have champagne tastes and beer income. Its not a bad idea for a peacetime army to have big dreams, but it can also mean that your doctrinal foundations are built on sand. When theory and practice bear little similarily, doctrine can become ignored. Some of our doctrinal discusions are akin to debating how many angels can dance on the head of a pin. More dangerously, we can sometimes argue about deck chair arrangement on the Titanic.
I apologize for the long post!
Red Five standing by...