It could be done but what's the point - the normal leadership process will kick off next week and take a few weeks to run its course, in the meantime the new cabinet that has just been appointed can keep the lights on.
The point is that we can't have a lying, incompetent, lazy narcissist in power for one day more. It is ludicrous to say that the cabinet can keep the lights on - this includes people like Patel and Zahawi both of whom have allegedly told Johnson that he does not have their confidence as PM. To say nothing of a load of inexperienced nonentities like Cleverly. How is that conceivably a functional way to run a country?
And how can we deal sensibly with other countries when our PM is someone 60 of whose colleagues have resigned citing his lack of basic integrity and honesty. To say nothing of his late admission of extremely dodgy dealings with Lebedev. The likes of Putin must be laughing their socks off.
If all that is needed is to keep the lights on, we can do that infinitely better without Johnson busily keeping his nose in the trough as long as he possibly can.