Are there groups of Basilisks, or even more than one? I know that there were one or two recorded -- Herpo the Foul bred one and obviously Salazar Slytherin's did as well. Were there any wild Basilisks which nobody found?
Per Fantastic Beasts and Where to Find Them, Basilisks are not bred; they are created by wizards. Herpo the Foul created the first known Basilisk by hatching a chicken's egg under a toad. Whether magic is also involved in this process is unknown; it doesn't say so. The only other known Basilisk in Harry Potter canon is Salazar Slytherin's Basilisk which lived in the Chamber of Secrets.
Because Basilisks are created and not bred, it would be impossible for a Basilisk to be born into the wild. So the answer is that there are no known wild Basilisks that went undiscovered.
It is clear that Rowling drew creatively from mythology and lore that has already existed for centuries - this is not a criticism as some take it, I very much admire Rowling for the spectacular story she wove together and the breadth of lore from which she drew - so if you want an answer that is non-potter universe, here it is. A basilisk appears in The Bible in Isiah 14:29 - although depending on the translation can also be referred to as a cockatrice. Basilisks are also mentioned by Pliny the elder in his "Natural History" in 79 A.D.
It seems that when people believed the creature did truly exist, they believed it to be a bit smaller than Rowling's Basilisk. Pliny describes it as "no longer than 12 fingers" and so poisonous that it could kill a horse of the rider that would also die if a person on horseback was to thrust a spear into it. Everywhere one went, everything around it was lit on fire or otherwise perished and cracked from the poison it left in its wake and so it is never found anywhere but sandy desert. For this reason, the belief is that some persons encountered and misunderstood depictions of the Egyptian Cobra.
It can be seen in church architecture and illuminated manuscripts from the middle ages and was a cross between a cock and a serpent. Some seem to distinguish the basilisk from the also fearsome mythological cross between a serpent and chicken, the cockatrice or cockatrix, but it seems to me they are really one in the same with different names from different cultures/times in history.
Whatever the case, in Greek Mythology it is said to arise when a seven year old cock lays a spherical and yolkless egg that is then hatched by a toad. Basilisks give birth to fire dragons so Basilisks cannot beget more Basilisks (besides the fact that in mythology they kill anything that sees them so I'd imagine mating rather difficult - but anyway).
Incidentally, basilisk is now the common name given to an entire family of lizards known by scientists as the "Corytophanidae."
Given this information, I would guess that if a wizard helped a cockerel to lay a spherical egg in its seventh year and a toad to hatch it (like apparently Herpo did), more could appear. It would seem not likely they would exist naturally however whether you use only book lore or the broader lore of the world.
If one assumed wizards and witches really surround us muggles and we just don't know it, Herpo must have created the first a VERY long time ago. I'd imagine a few evil wizards have figured out how to create them in the interim other than just Slytherin, but they would certainly be rare and easy for a ministry official to detect before too many of us Muggles could encounter it. Since essence of weasel will kill the creature, I would think any protective or defensive ministry or governmental entity regarding dangerous creatures would have it killed immediately. Certainly deserts would suddenly arise where they shouldn't exist giving away its existence and where-abouts when not trapped far beneath the stony earth and a magical and grand lake - hmm. . . Perhaps an explanation for desertification that has not been considered?
A quick search of "Basilisk Mythology" will yield more sources as well, but these are some of the best.
In Harry Potter, there is only the one Basilisk, as far as we know. The one in "Harry Potter and the Chamber of Secrets" is the same one that Ron and Hermione see during the Battle of Hogwarts in "Harry Potter and the Deathly Hallows." This is most likely the case, because earlier in the book Ron, Harry and Hermione were talking about how only extremely powerfully magical objects could destroy a Horcrux, and the venom in the Basilisk's fang is just that: extremely powerfully magical.