Is it possible to expedite Motion to Reopen a H1B petition after denial (such as premium processing)?

Sorry, it appears to be too late to file for premium processing ... expedite isn't an option. Talk to the lawyer that did the paperwork to explore all of the employer options.

You can appeal with the AAO-Administrative Appeals Office but must still send to the USCIS office who denied the case and they will then certify the case and send it to AAO in DC. You can file motion to reopen or reconsider or both concurrently. Unless you have new compelling evidence, or something minor was missed etc. then perhaps the Appeal is the better option for you BUT, these are just general guidelines and you should not rely on them since I do not know you case, have no facts, don't know the reason for denial, etc. If you want a definitive answer, call or email me for a consultation or contact other colleagues on this site, and furnish them with all the information thats pertinent. Also, remember there are time sensitive deadlines and if you missed them you may not late file and your case becomes final. Be very cautious. Also, when you appeal or reopen/reconsider, if you ultimately prevail USCIS will go back and grant your H-1B from the outset BUT if you loose, you will not have accumulated even more time out of status, so its a gamble. regards.

Appeals of denial decisions, and that includes Motions to Reopen/Reconsider cannot be expedited. An Appeal or MTR to the AAU presently takes about a year and a half to be decided and in 4 cases out of 5 the AAU sides with the government and denies the appeal. The fact that you have an appeal or MTR filed and it is pending does not give you the legal right to remain in the U.S.,