表示主动动作

The company is expanding with new projects every quarter.

（公司每季度都在开展新项目，表示主动进行。）

表示被动状态

The meeting was postponed with the report not being finished.

（会议因报告未完成而推迟，表示被动关系。）

描述伴随状态

She walked to school with her cat chasing a ball.

（她走路去上学时，猫在追球，描述同时发生的动作。）

表达原因或条件

The project was delayed with the supplier failing to deliver on time.

（项目因供应商延迟交货而延误，说明原因。）

补充说明

The chef was praised for his dinner with the flavors perfectly balanced.

（主厨因晚餐调味恰到好处而受到称赞，补充说明动作结果。）

通过这些示例，可以看到"with sth. doing"结构既能表达主动动作，也能体现被动关系，需根据语境选择合适形式。