Each of the three is different in their own way; each has their own style. Expresses individual differences or variety.
子供たちは三者三様に遊んでいる。
The three children are each playing in their own way.
新入社員の反応は三者三様で、先輩たちはそれを楽しんでいる。
The new employees' reactions vary — each in their own way — and the seniors find it amusing.
デザイン案は三者三様だが、どれも魅力がある。
The three design proposals are each different, but all are appealing.