The company which was created in the summer of 1999 would not have many of the same men left by the time the company celebrated the 20th anniversary celebration.

原句在by the time 引导的时间状语中，动（celebrated）宾（celebration）重复，应把celebration 直接删掉。让the 20th anniversary 作宾语！

这样才正确：by the time the company celebrated the 20th anniversary.（到公司庆祝成立20周年时）

The company which was created in the summer of 1999 would not have many of the same men left by the time the company celebrated the 20th anniversary.

【翻译】这家成立于1999年夏天的公司，到它庆祝成立20周年时不会有很多人留下来。

the same men 指公司成立时的“原班人马；老员工”，意思清晰，不缺成分。left by the time the company celebrated the 20th anniversary，作the same men 的定语。