I am not too sure why you wish to file a petition for H-1B twice.
Since you have done Master's from a U.S. University, you may be eligible to apply starting March 8 under the cap-exempt 20,000 H-1Bs. The petition can initially be approved for 3 years and can be extended upto a maximum of 6 years (in certain circumstances beyond the 6th year too). Thus you may not need to file a new petition if you continue working for the employer who petitions for you.
In case you find a new employer, you can transfer your H-1B by filing for H-1 transfer. That will NOT be a new petition but an H-1 transfer. You can transfer your H-1 from one employer to the other from within the U.S.