You can hold both a SI medical certificate AND BasicMed at the same time. However, you're on the hook to comply with the Special Issuance Authorization Letter (SIAL) for as long as the underlying Special Issuance Medical Certificate (SIMC) is valid.
Now...AND THIS IS EXTREMELY IMPORTANT...you MUST comply with the terms of the SIAL all the way up to and through the expiration date of the SIMC. Any and all medical information required to be submitted by the SIAL must be submitted all the way up to and through the expiry date on the SIMC. You would normally do this when you go in to renew your SIMC. You're still going to go in and submit the information, but you're not going to fill out a MedXpress application, nor will you be doing a physical.
As
@Brad Z, our resident FAA guy, once said, once the medical certificate is timed out and that final medical information submission is complete, DO NOT SEND ANYTHING to FAA Office of Aerospace Medicine unless you intend to renew the medical certificate.