Tricky question there. Whether she is "allowed" and/or whether you will be paid are 2 separate questions.
If she is only credentialed with BCBS and billing is under her name, any other insurance will be processed as out of network (which could mean denied, applied to deductible, etc.)
She is "allowed" by her training and state policies to treat and care for patients.
I STRONGLY recommend you immediately begin the process of her credentialing with any other insurances that your physician participates with.
From a previous of my posts - Here is my personal recommendation when you have a new provider (whether NPP or physician) who is not yet credentialed.
1) Submit credentialing ASAP. I try to do this before provider has even started. I start the process the day the employment contract is signed.
2) Until that provider is credentialed, you need to make a business decision about what work they provide. I try to maximize the amount of work they provide that is either not paid or billable correctly. Examples of work not paid: postop visits, rx renewals, patient phone calls for triage or results, afternoon hospital rounds after another clinician rounded in the morning. Once they start becoming credentialed, keep an updated list of those insurances and funnel patients with those plans to the new provider. Schedule all self pay patients with this new clinician.
3) If the new provider is an NPP, schedule as much as possible that could be billed incident-to a physician. There are a few rules about this, so make sure you are following them. For example: physician must be onsite, treatment plan must already be determined by physician, etc.
4) If you have any commercial carriers that do not credential NPPs and want services billed under physician, that is another option. Side note: this used to be common, but none of my current carriers want this. Your contracts/carriers could vary.
5) You may decide it is in the best interest of patient care and the practice for this clinician to sometimes provide care that you know you will not be covered under insurance. You could decide to provide the services for free. Create a dummy code in your system that does not get billed to insurance to track the work for your own knowledge (provider metrics, etc.) You could inform patients that the provider is not credentialed and they would be billed for any insurance applied deductible/co-insurance. I would have them sign an acknowledgement of this. Some carriers could require a specific form for this.