你的句子中的 with 不是表示伴随，而是表示“与……有关”（= used to say what an action or situation is related to）。即 His business is with other men's money 的字面意思是：他做的生意与别人钱有关。

with 表示“与……有关”的更多例句：

We have a problem with parking in this area. 我们这里有停车问题。

Is there something wrong with your phone? 你的电话出什么问题了吗？

How are you getting on with your studies, David? 你的学习怎么样，戴维？