I have a low quantity book project that will need a book sized A3 with 1000-1500 pages. Is there a print on demand provider out there that could possibly handle that?
They exist. Though it depends where you are.
A3 appears to be art book sized.
The A3 size print measures 29.7 x 42.0cm, 11.69 x 16.53 inches, if mounted 40.6 x 50.8cm, 15.98 x 20 inches. (ref)
Why does it talk about mounting? Because it's a designation for art prints, not books.
A3 is a paper size that is typically used for drawings, diagrams and large tables. It is also frequently used in laser printers to output two A4 pages as a spread....A3 measures 297 × 420 millimeters or 11.69 × 16.54 inches. In PostScript, its dimensions are rounded off to 842 × 1190 points...
In the American market ISO paper sizes are hardly used at all. The US-alternative to A3 is called Tabloid or Ledger (ANSI B) and measures 11 x 17″ or 279 × 432 mm. (ref)
So why A3? Will 11x17" do? Are you outside of the US in a place where A3 is commonly used for books?
As for the page count of your book, that's going to be really heavy. Especially if you're using quality paper which is heavier. And then there is the larger dimensions. Will anyone be able to lift your book? Perhaps you want multiple volumes?
Some can do A3 size.
Unaware of any that can do 1000-1500 pages. Even real publishers do not normally do that.
Your best bet is to cut it to smaller volumes.
Or you could print but not bind the pages with many book printers or copy shops and then take them for binding to a bindery that could do a book that big.
But you seriously need to rethink the need for even having a book with that many pages at that size.
Those links someone gave above show a 12x12 maximum, and the other one had a page limit. Each may have other restrictions.
Your book is overspecified and you must compromise to make it feasible.
Better late than never...
The realistic answer to your question is NO. Tabloid / A3 is much larger than reasonably priced POD houses can handle. You might have to try a company that specialises in large books, like atlases.
Alternatively, you can go down the Do It Yourself route. Most local printshops (in the US, Staples, Office Depot or UPS Store) can handle tabloid sized paper. I'm sure their counterparts in Europe can handle A3. If you don't want to drill a/o punch holes in the paper yourself, just have them use pre-punched paper. You might even be able to get them to use your own paper, so long as it's compatible with laser printers.
I recently finished an "art project based around writing" myself, a work of fantasy geopoesy. No POD book makers can handle tabloid, so it was off to the UPS Store for me!
Once they printed it, it was just a matter of binding & making a cover. I use a modified Oriental binding stitch for the pages, and cloth tapes to attach the book boards and glue for the end papers & leather cover.