We worked in the same office that would be convenient for us to meet each other.

这个句子是个错句。that占据了从句主语的位置，说明that是个关系代词引导定语从句。当先行词被the same修饰时，通常定语从句由as或that引导。但这种定语从句是限制性定语，说明先行词是与另一个人或者事物相同的或同一个人或事物。但本句中的从句并没有这种比较或限制的意义，而是补充说明情况，因而是非限制性定语。that不能引导非限制性定语从句。即使改为which，指代先行词office，从句的意义为office is convenient也不符合逻辑。

这个句子可作如下修改：

We worked in the same office. That would be convenient for us to meet each other.

that为指示代词，指代前句的内容。

We worked in the same office，so it would be convenient for us to meet each other.

so为并列连词，表示因果关系。it指代前句内容。

We worked in the same office，which would be convenient for us to meet each other.

which引导非限制性定语从句，先行词为主句内容。

We worked in the same office，where it would be convenient for us to meet each other.

where引导非限制性定语从句，先行词为office，it为形式主语，不定式复合结构作真正主语。