Information regarding Cuncurrent VISA

I work for a cap-exempt employer (UNiversity) and I have a job offer from cap-subject employer (Company). Since my new employer is cap- subject so I cant start working for them immediately and I will have to wait until October. However, my H1B application filed by my company reached late (June 12) and hence no H1B from company side for this year fiscal year. My lawyer has suggested that I can file a concurrent H1b petition so that I can start working for a company as well as University till next year and next year my company can file the H1B in April-2013.

My question is:

  1. Is this possible?
  2. If possible, then what is the procedure?

Please reply at your earliest. Any input will be appreciated Thanks.