It is an
absolute that only one of a species can be kept in a tank. Even with dividers, multiple species do not do well together and show aggression.
There is one known exception among the commonly kept species if the animals were found together or are siblings. The dwarf, Octopus mercatoris has been successfully raised in small groups. It is unclear if two strangers are placed together in a small tank if both will survive but hatchlings and octopuses found in the same live rock have proven to work well. They will inbreed (and likely do in the wild) and produce viable young. The number of successful inbred generations is unknown but we have journals on a few WC female ->tank raised (wild fertilized)->tank bred families.
In VERY large tanks, O. vulgaris have been successful (not home volumes) to a point with a few casualties when size differences were present. Mating has occurred but vulgaris is a small egg species and the hatchlings never mature.
A newly described species, current common name
Larger Pacific Striped Octopus lives together in situ and seems well suited for the aquarium. Sadly, they are not plentiful and should not be harvested for pet keeping (but I will dream about a captive breeding program. Sadly, this is a small egg species so the chances are slim and none).
A third (cousin to the Larger Pacific Striped) potential is the O. chierchiae. There is no published evidence that these would survive together as the current experimenters have avoided (last I asked) attempting it because the animal is rare. We do know they will mate in captivity (introducing the male only for a mating attempt under supervision and removing him after mating or sensed rejection) and produce large eggs so there is hope in this species for something we can eventually tank raise. In addition to being a nice size and attractive, this is one of only two known (the other being its cousin) species that can produce multiple clutches. Exciting in the area of keeping but a long way from tank raising for the home aquarist.
So, in a practical sense, the current answer is no with the exception of O. mercatoris siblings.