USCIS never limits petitions a person can file. you can file family based and employment based petition at the same time.
But since you've have a EB2, to pursue a EB3 where the PD is far behind EB2, not a wise move.
There is nothing called maintaining the first EB3. For the LC, if your employer did not provide the necessary info to process the info, it will be closed after 45 days.