I already have an L-1 at the company I work at, but that doesn't allow me to work elsewhere. Does make anything easier?
To change jobs on an L-1 you really need to have filed I-140 and be on the way toward your Green Card.
https://www.uscis.gov/policy-manual/volume-7-part-e-chapter-...
What this means concretely is if you have an L-1, an approved I-140 filed >6 months ago, and you’re now pending Adjustment of Status, I think it’s fairly safe to change jobs under AC21 (that’s what I did; this is not legal advice and I’m not an attorney, I took legal advice about my situation).
If you change jobs to work for Employer B after I-140 has been filed and >6 months has passed but *before* it is approved, I think that’s technically allowed in an authorization to work sense, however your L-1 is no longer valid, so if your I-140 filed by Employer A gets an RFE or Denial, you may be in difficult territory.