Cheap helmets tend to come in 2 helmet shell sizes and the typical range of four sizes S, M, L and XL is simply adjusting the thickness of the impact absorbing lining with S and M using the smaller shell and L and XL the larger shell. You may even get some helmets that squeeze in 3 sizings per shell size XS, S, M, L, XL, XXL. This MAY affect the quality of the fit across the range as does a person's individual head shape etc which may suit some helmets better than others. Historically Arai had more oval shaped helmets where as Shoei had rounder ones. There are all sorts of variations by brands and helmets and these old rules of thumb may not exist anymore and helmets should be tried for fit before buying.
Better quality and more expensive helmet brands usually have at least three shell sizes with no more than two sizings in each shell size, XS, S, M, L, XL, XXL. Therefore the variation in absorption lining thickness is less and a better fit MAY be obtained. These issues are likely to be exacerbated in modular helmets which already tend to be larger externally to cater for the fitting of the modular joint.
Some people dislike big 'Basketball' sized helmets but they possibly have thicker shock absorption layers but they may also use cheaper Styrofoam, expanded polystyrene type instead of the much more modern and technically improved materials. For maximum risk reduction you would be wise to consider multilayered designs that allow slippage between them so the rotational force transmitted to the skull is much reduced and slowed down hence reducing brain inter-cranial movement intensity and associated damage.
e.g. The now old but still available Lazer Superskins in full face and jet style. Now extremely cheap new on eBay from Germany or Austria for under $100 (they used to be $400) I have posted about them before, so do a search in the forums posted by me or go to webbikeworld.
@HansO was wearing an open face one and it worked as designed and he had no brain injury at all after a very big crash earlier this year with the thin flexible lubricated outer skin moving and then tearing away leaving the shell underneath unmarked. The real focus of the design is to reduce brain rotation inside the skull which occurs when the outer surface contacts something and grips it momentarily causing the still moving brain to spin and slosh back and forth inside the skull.
6D ATS-1
ATS-1 has Omni Directional Suspension (ODS)
Bell's:
MIPS, or Multi-Directional Impact Protection System found in the budget Qualifier DLX full face range
Qualifier DLX MiPS-Equipped - Helmets - Powersports | Bell Helmets
Comes in a XXXL65-66 cm25" - 25 1/4"8" - 8 1/4"
Rotational Energy Management creates a "slip zone" within the liner to allow for subtle movement between the liner layers to reduce rotational energy transfer.
PRO STAR
Bell Pro Star Helmet
FLEX IMPACT LINER: Pro Star and Race Star helmets feature the Flex impact liner, a first-of-its kind, three-layer impact liner designed to manage energy from three potential impact scenarios: low, mid and high-speed. It does this by using three different materials at three different densities. As the impact becomes greater, higher density layers are engaged to manage energy.
In the old days helmets were more focussed on resilience of the shell itself rather than the jello sloshing around inside it.
As
@barbagris said a good read of the various Standards websites, SNELL, DOT and UK Sharp as well as the webbikeworld link he provided may assist.
Norm - go here and select TYPE OF LID and 5stars
https://sharp.dft.gov.uk/ - some of the lids may not be available in the US - but it's a start. Would also suggest a perusal of
Motorcycle Helmet Reviews - webBikeWorld
Recently the law was amended here in Australia allowing the use of helmets with US SNELL, DOT; EU ECE 22.05; and UK SHARP standards approval as well as the existing AS/NZS 1698.
I would expect only the better quality and expensive brands would cater for the extreme sizings such as XXS and XXXL and I have never seen XXXXL listed.
So
@BigNorm sad to say but true your big head means the shock absorbing layer in your helmet will be less than that of someone with a smaller head in the same size shell. It may still pass the testing standard but a lot of the standards tests may only be conducted on a range of sizes within a brand/model and you may need to check with the manufacturers of the very big oversized helmet you require if they have actually tested it to the standards in your size. To the happy and good however, I also think you may find that only the better quality and more expensive brands are likely to cater for your size in any case. Avoid cut down basketballs with cheap foam linings.

This other green vegan version may cool your head and fit if you get a big one but hardly recommended.