between different organizations for people who share similar interests

The Horticultural Society and the Botany Association are planning to hold an inter-society vegetable-growing competition.

I spent hours preparing for the intersociety debating contest. 我花了好几个小时为社团间的辩论赛做准备。

between different human societies

We should be aiming to restore inter-society equality.

Looking at Europe and the Middle East, there are notable intersociety differences in the employment of women. 纵观欧洲和中东，妇女的就业情况存在着显著的社会间差异。