H1B Transfer 问题(大学=>公司)

现在身份是NON-PROFIT 的H1B。将申请10月一号的H1B TRANSFER。但公司希望我能更早工作。是否有什么办法可以这样做?

For example,
1. is there any grace period between transfer? So, I can volunteerly work for the company.
2. applying for no-paid vacations from the university, and volunteerly work for the comapny till October 1st.

Are these two ways possible? or is there any better ways in which I can work for the company earlier than october 1st?

Thanks so much!