https://www.spotrac.com/nba/boston-celtics/cap/2023/Important to look at our 2023-24 season cap sheet if you're talking a Grant extension.
Right now, we are at $130.7M in salaries. I also wouldn't be surprised if we decline Nesmith's 4th year option which lowers that by $5.6M. Thei as an expiring $9.1M is pretty movable too since he'll be expiring (year after is team option). The projected tax line is $156.45M. The tax apron will be about $5-6M higher than that. The tax apron is what you become hard capped at if you execute a S&T or want to use the full MLE. So even before any subtractions, we have about $30M to spend up to the hard cap and only Horford is a FA amongst our top 10 current players (and he'll be 37 so you figure his market is somewhat limited and thus cheaper).
We are a real threat to do a S&T next year for a significant free agent. If you re-signed Grant to the type of deal that people in here are suggesting ($12-14M/year), then Grant/Theis/Pritchard give you about outgoing $25M. If Nesmith is still here that's $30M you can send out and all of it beside Grant would be expiring.
People keep talking about Bradley Beal... if he were a FA next year instead of this year then all of this S&T math would be a LAYUP, so long as Grant is extended to use in the deal.
If you don't sign Grant now, then you won't be able to practically trade him next offseason. His restricted free agency, base-year compensation rules, etc. make it extremely difficult to do and requires sign-in from him on where he goes.
I'm not saying negotiate against yourself, but push comes to shove, we're better off just caving and signing him for an extra $1-2M/year vs. playing hardball and letting him go to free agency. We lose incredible amounts of upside and flexibility if we hold hard at $10M/year vs. caving at $13M/year like some people in here say.