Well, filing multiple COS applications at the same time will confuse the USCIS officer judging your case. Think about it, if USCIS sees this person want to Change to L1A and also to H4, how can you change to both at the same time ? The easier thing to get H4 is to exit and get H4 stamping, which is easy and straightforward without much issues. Discuss with your attorney on the best way to put up your case with COS to avoid rejection or plan for other options…
@Kumar I have little different situation and need your guidance for the same:
Currently My employer applied for COS from L2 EAD to H1B , Still case is in progress . So can I work on receipt number till my COS to H1 gets approved ( it is with same employer) ?