Only if he can come up with a "new" argument. All previous arguments were shot down by the lower courts and upheld by the USSC.
Any new arguments would be guided by previous USSC and Circuit court decisions as applied to normal people, in other words existing case law, which is well settled when it comes to ordinary individuals.
How long would you expect that process to last?
In the Cy Vance (NY DA) case, the first of two cases handed down. It would take as long as any normal court docket. Right now the accountants / banks have to obey the grand jury subpoenas served them within the original time limits set in them. And for which they raised no original objection to.
Any delay would have to be by motion giving new reasons, limited to exiting recognized case law, which Trump already lost.
But Trump could file a motion to invalidate the subpoena just like he did before losing at the district court, and the circuit court and then at the USSC. But would just take until the next motion hearing to throw it out.
In short, Trump has no better argument to stop the release of those records to the grand jury, than you or I have. And its only a matter of administrative delays, ex: transfer of paperwork from USSC to circuit court to district court.