I-140 approved + end of H1, wish to change jobs

[vinsus]

Hi,
This is my current status:
- Company A applied for EB-3
- PD is Aug2007
- I140 is approved
- 6th yr of H1 gets over in Jul'09 (company A will file for extension)
- EAD not applied

I am planning to change jobs sometime in May-June timeframe. I am not claer whether I can legally change companies?
Questions:
1. What are the options for me to change comanies at this stage?
2. Can new employer transfer my H1?
3. Should I be changing jobs only after I get an EAD?

Thanks in advance.