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I'm picturing the Greek Phalanx formation, where soldiers were arranged in rows and the men in Row B or even Row C could attack the enemy by thrusting their spears between the soldiers in Row A.

Can you do that with a Reach weapon in DnD 5e? Attack an enemy even though there's an ally (or even a row of allies) directly between you and them?

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Yes, but they will have half cover

The rules on cover are listed here. The total cover rule is the only one that prevents attacking:

Total Cover

A target with total cover can't be targeted directly by an attack or a spell, although some spells can reach such a target by including it in an area of effect. A target has total cover if it is completely concealed by an obstacle.

Allies don't give total cover though, they give half cover:

Half Cover

A target with half cover has a +2 bonus to AC and Dexterity saving throws. A target has half cover if an obstacle blocks at least half of its body. The obstacle might be a low wall, a large piece of furniture, a narrow tree trunk, or a creature, whether that creature is an enemy or a friend.

So you can attack "through" an ally but the target will have half cover from the attack.

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