Ask a HVAC professional that can see what you are planning to build. Every house is different.

The warm or cool air you blow into the space needs a way out, so most production builders use a "transfer grill". A cheap solution consisting of grills on either side of the wall to let the air escape.

Having returns for each room is a better idea, but is more complicated, more ducting, more labor. $3750 sounds like a pretty good deal if it's worth it to you.

In the southern U.S., central HVAC returns are common. It is our standard practice to install a return in each bedroom to promote proper air flow and ensure occupant comfort.

In Minnesota we had returns in all bedrooms plus two large returns. Here in Washington I was informed one large return was customary.

I would prefer them smaller and scattered around.

Supplies in every room, returns as needed. $400 per added duct may or may not be unreasonable but I would instead recommend a Honeywell Zone system, which would give you 3 thermostats per system, and allow the system to focus energy on the impacted area. It may need 2 more returns.

We have a 4500 square foot house and have two returns. We then have supplies in every room, some with more than one. The returns are the bigger ones not the little ones on the floor or ceiling of each room

Sorry we have three. One in each floor.

If you have concerns about your builder's approach, have a mechanical engineer design and spec your HVAC . This has been a legal requirement in our jurisdiction for decades. Maybe not so elsewhere.

It may turn out that your builder's method is best. For instance, Building Science Corp. notes that a "central 'hard' ducted return that is airtight and coupled with transfer grilles to relieve bedroom pressurization significantly outperforms a traditional return system, which has leaky ducted returns in every room, stud bays used as return ducts, and panned floor joists."

For a current planned build of 8,550 conditioned sf the mechanical engineer has speced hard ducted returns for each bedroom, but keeping them tight with mastic sealant. No undercut doors, No jump ducts or transfer grilles.

Experts....what is the 'code' requirement? Is it somehow different for each state?

ditto what worthy said.

OK....maybe here:

https://yellowbluetech.com/hvac-codes-and-standards/

Air flow is important that is why returns are installed. Nobody can guess an estimate without to be on the place.

Code definitely varies.

Last build - 10 years ago - large central returns. Quoted $1000 or so for bedroom returns - part of that was central filter - rather than at returns. I didn't do it. 4,000 sqft - 4 bedrooms - 2 story.

This build - returns all rooms. Each 12x12 with its own local filter. The filters get so little air flow that they stay very clean and don't need changing that often.

Are your ducts in conditioned space? - because if not - the central return would likely minimize duct losses. Just a consideration. $3750 seems a bit high to me but not excessive and you don't mention what your ducts are - certainly rigid cost more. If you are held to a high standard for duct leakage, that would increase cost.

In some jurisdictions, duct leakage is tested. For me, Energy Star had different standards for conditioned vs. unconditioned space. So lots of unknown variables.

Previous home had 5500 sq ft. We had 2 large returns on first floor. 3 small returns on 2nd floor, and 1 return in finished basement.

For new home where we have 3800 finished, we will have2 medium returns, both centrally located, on the main floor. That floor is fairly opened to other rooms, plus the staircase is opened to the upstairs. We will have 1 medium return on the second floor.

In all of the homes we have lived in, we have never had returns in the bedrooms.

Apparently the norm for cold air returns varies a lot across the country. We had a single story 2600 sq ft house built in San Antonio and they used two A/C units. There is a large return for each unit in the main living space and one return in each of the four bedrooms. All the returns come into a main plenum on each A/C unit, where they connect to a large filter unit.

Bruce