You can, but they would be entitled to a percentage of the attorney's fees, so a new attorney may be unwilling to take a reduction. If B&B were to drop you voluntarily, then they would be entitled to no fees. (Becoming a high maintenance client can encourage this.) SS determines which attorney gets paid what amount, and you can always argue they did a poor job representing you and should receive little to nothing. You need to read your contract with Binder and Binder, which might allow them more than the normal $6000 max since they represented you at the AC level.
http://www.disabilitysecrets.com/res...ition-get-paid.

Even half of the fees would be better than starting over from scratch where you'd have no back pay and are ineligible for SSDI--they would be unlikely to take you on until you're a few years into the process. --Although, apparently they can do a fee petition even in that scenario, but I've never heard of that happening to someone.

I'm unclear if you're considering new council before your ALJ hearing, or only if you're denied again?

You can see if B&B would be willing to reassign you a new attorney. Or, if you're happy with the senior attorney, you can ask to work more closely with him/her.

There are some advocacy groups that will help you at no charge. They are generally for those with psych or mental impairments, and you'll most easily find them in large urban locations.

Have you received a hearing date yet?