Applying for L1 Visa while having an approved H1B Visa (not stamped)

[asakin]

Hi,
Company "A" is applying for an H1B on my behalf with start date of October 2013, with an option to delay my start date until Aril 2014.
My current employer (Company "B") just offered me an option to relocate on L1 visa around May 2014.

My question is:

Assuming that my H1B Visa for Company "A" is approved, and I don't relocate before April 2014 (and don't stamp the H1B visa), will Company "B" have any trouble applying for an L1 Visa on my behalf?
Am I able to keep both employment options open (Company "A" and Company "B") until April, given that I don't stamp the H1B visa before that, and decide a few weeks before the actual start date?

Thanks,
Arik