Weekends, they have to pay the engineer and the conductors the same hourly rate. They don't have any RDCs. The HSP46s are overkill to pull a coach or two, and the older engines are ready for the boneyard, allegedly. Without weekday rush hour CR service, many commutes would become impossible and people and companies would move elsewhere. Nothing depends on the weekend service. You can drive the speed limit on the Mass Pike and I-93. In fact, they should eliminate weekend CR service and use the money for even bigger legislative pay raises
What does weekend service have going for it? CR on weekends is faster than the rabid transit. With long headways between subway/trolley/bus service, you could possibly spend less time waiting for a CR train running on an accurate schedule than subway/trolleys running semi-randomly.
Weekend solution? Make parking free. Acquire some refurbished RDCs. Install automatic doors and Charlie Card fareboxes. Negotiate single train operation with the union for these weekend one or two car RDCs when <100 passengers are expected, and minimal number of conductors when >100. When in single operator mode, use front door only and high-level boarding only. Reduce fare to match rapid-transit fare for the same distance. Offer cheap family fares for 2-6 riders weekends and off-peak. Reduce weekend fare to about 1/44th of the monthly rate.
Concentrate on short-turn runs out to about 1 stop or so past 128: Wellesley on the Framingham line, Canton Juncton on the NEC, Dedham Corporate via Fairmont. Anderson to the north, Roberts on the Fitchburg. Lynn. Express Braintree-Quincy-BOS. This would be a great way to experiment.
As for the original subject of the thread, have large events subsidize the extra T service as part of their budgets. Force paying conventions to include Charlie Cards preloaded with unlimited day passes for specific days.