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?