A few thoughts, from someone who has both printed such sizes and mounted them.
You can get 4 x 8 (48 x 96) foam core, in 1/2" and for a print of that size I would stay with either foam core or Gaterboard. Gaterboard is not archival, as it has formaldehyde in it's make up, but it's quite strong. If you are printing on a RC paper you should not have any issues. The largest dry mount press I have used is a 4 x 8 (which allows for mounting to a 4 x 8 sheet of foamcore or gator. You need to have a good shop that knows what they are doing, as it's so easy to get dirt under such a large print, and once pressed, it will show up immediately.
For such a large print, I would not go full bleed, at you will have all types of problems, both in just handling it off the printer without getting a smudge on it and mounting it. Leave at least 1/2" to help in handling. You will also have to use extreme caution in just rolling up the print, to prevent a v crease, which will easily ruin a large print, even dry mounted.
As for Plexi, sure it can be done, but at a huge cost and only by a good lab. I would never attempt that by myself, as you need a perfectly clean room to mount face mount (if that is what you are referring to).
If you are not thinking face mount then you have to consider glazing and that will be a huge issue, both in cost and weight. 40 x 100" piece of glass is possible but so very hard to work with, not to mention transport or ship. Many folks would move to plexiglass for such a size. Again, huge issue as plexiglass is covered on both sides with a protective paper, once pulled off it's a static magnetic sheet for dust. Extremely hard to clean and mount without dust showing up. It can be done, but it has to be by a shop that has working knowledge of the product.
Other options.
Print on metal, companies like Bay photo have an excellent metal printing process, and I believe you can get to that size or close with a custom order, again won't be cheap.
Print on canvas, and then mount to gator after coating. I have 20 or so 4 x 8 size canvas prints in various locations in my state. All were printed on canvas, coated, then mounted to gator, and then placed in a simple metal frame for mounting. The canvas when coated is extremely durable and much lighter than any paper solution that will have glazing. You can also go full bleed on the canvas as the issues of handling are IMO easier than paper.
Just some thoughts, you will get a ton of other ideas. But this has worked well for me.
Paul Caldwell