wanna_gc:
IMHO, working on 1099 should be OK since I've seen RFE text read something like 'Please furnish W-2/1099...' which people misinterpret as 1099-INT, et al. Please check with your lawyer. My lawyer said it was OK as long as the job is in the same or similar category as your original LC job.
Is your employer asking you to work on a 1099? Are you currently on a W-2? Though working on a 1099 will save your employer $$ it will add to your tax burden since you'll need to pay IRS the employer's share of FICA (SS & Medicare tax), which is to your disadvantage especially if you have an employer-employee relationship. If you're status is truly that of an independent contractor (see IRS 20-point rule, will post link later) then it's OK to work on 1099.