Questions about F1 OPT TO H1B conversion.

[kumark.engineer]

I'm currently on the OPT period of my F1 (Have taken the 27 month STEM extension, and this is valid till November 2014). I work with a Mechanical Engineering firm as a Contractor through a contracting company. The company had agreed to take me on as a full time employee, and apply for my H1B visa, which needs to be done by April 2014. Due to some unexpected situations, there might be a possibility that my company may not be able to take me on as a full-time employee soon. The contracting company that I'm with does not sponsor new H1Bs, and hence, they can't be my sponsor either (But they do transfer H1B visas over). If I'm able to find a different contracting firm, can the contract be transferred over to the newer firm, and have them be the sponsor of my H1B ? What are my other options ?