Describes acting in unison or as a single entity. Often used in formal or literary contexts.
彼らは同体になって問題に取り組んだ。
They tackled the problem as one.
家族は同体に暮らしている。
The family lives together as a unit.
From 同体 (どうたい, 'same body') + adverbial particle に. The exact historical derivation is uncertain, but the meaning is transparent from its components.