Example from a 2017 website:
数多の数ある猫種、是非お気に入りの猫ちゃんを見つけて下さい。
Question: In what order of magnitude would you expect the number to be?
Or, since it probably depends on the context, what would the closest English expression be?
Also spelled "あまたの数".
あまたの～ is a literary way to say "a vast number of ～". The exact number can be a million or a hundred depending on the context, but it's stronger than たくさんの, anyway. If this is an ad of a pet shop, I would feel they are quite confident about the variety of cats.
You can say あまたの猫種, あまたある猫種 or 数ある猫種, but I feel 数多の数ある猫種 is a little strange. 数ある on its own means "many", so it sounds like "a vast number of many kinds of cats" to me. BCCWJ has more than 100 entries of あまたの/数多の, but no example of あまたの数/数多の数.
The page you linked says あまた is a 熟字訓, which I agree. 数多の数 should be read あまたのかず.
In my opinion, "a large number" is simplest and best in this case.
However, I think it's impossible to put an objective magnitude on it because it's always going to be a relative term. Just as in English, "a lot" could be basically any number depending on what the context is. But since we are specifically talking about cats, and there is generally considered to be around 50 breeds of cat in existence, I think we can use "a large number" because it offers prospective owners a large variety of options to choose from when deciding on their desired breed of cat.
On a side note, is 猫種 actually a word? Sure the meaning is clear, but this term is not listed in several dictionaries I tried, such as here at Weblio.
