You can divide the types into three groups:
Group 1: types that are super effective against themselves (Ghost, Dragon)
Group 2: types that are neutral against themselves (Normal, Fighting, Flying, Ground, Rock, Bug, Fairy)
Group 3: types that resist themselves (Poison, Steel, Fire, Water, Grass, Electric, Psychic, Ice, Dark)
In order for a type combo to exist where both STABs are super effective against itself, you can immediately disqualify any combo that involves a type from group 3, because even if the resist is offset by an SE against the other type, that still can't increase the overall type multiplier beyond 1.
As there are only 2 types in group 1, there's only one combination to consider while staying within that bracket. Neither Ghost nor Dragon interfere by resisting each other, so that combo (which is unique to Giratina) does fit the bill.
Combining a group-1 type with a group-2 type comes up short: the only other type that could be SE against Ghost is Dark, and that's in the forbidden group 3. Meanwhile, two different types could provide SE against Dragon: Ice (group 3) and Fairy (group 2, but ruined by having a full immunity to Dragon).
Finally, in theory you could accomplish this with a pair of group-2 types that are mutually SE against each other, but no such types have ever existed: even discounting the group buckets, the only mutually super effective combos were Bug vs. Poison in RBY only (where Poison was group 3 in any case), and the trivial reflexive cases of Ghost vs. Ghost and Dragon vs. Dragon, which is the entire definition of group 1. That exhausts all the remaining possibilities, so Giratina is the only species with the honor of hitting itself SE with both of its own types.
In the NVE department, we can't quite summarily dismiss the types of group 1, because immunities exist and a 0 can offset any 2 to remain immune instead of neutral. Indeed, the Normal/Ghost combination is uniquely immune to both of its own STABs, the only problem being that no Pokemon of that type currently exists. Dragon also has an immunity, but Dragon/Fairy doesn't qualify here because Fairy ends up being SE to that. Now that group is conclusively out of space, and we can turn to the other possibilities.
Type combos consisting of two types in group 3 that don't interfere with each other (a ^ means a type combo that has no existing representatives): Poison/Steel^, Poison/Fire, Poison/Water, Poison/Electric^, Poison/Ice^, Poison/Dark, Steel/Water, Steel/Grass, Steel/Electric, Steel/Psychic, Steel/Dark, Fire/Electric, Fire/Psychic, Fire/Dark, Water/Psychic, Water/Ice, Water/Dark, Grass/Electric, Grass/Psychic, Grass/Dark, Electric/Psychic, Electric/Ice, Electric/Dark^, Psychic/Ice, Ice/Dark. On top of this, Steel/Fire (which would not otherwise qualify) has Heatran as its only representative, and Heatran has Flash Fire as its only legal ability, so it succeeds in double-resisting Steel while being immune to Fire. Likewise, Volcanion (the only Fire/Water type) always has Water Absorb to make up for Water being neutral by the type chart alone. That makes a total of 67 species and forms from among those that are capable of existing outside of battle.
Turning to group 2 alone for the moment, Bug/Fighting is the only combo from among those seven types that mutually resist each other, which is the necessary condition to get a match from that group alone. That adds Heracross, Buzzwole, and Pheromosa.
Finally, there are the combos involving a group-2 type and a group-3 type. There are several of these to check; the ones that actually pass are Poison/Fighting, Poison/Bug, Steel/Normal^, Steel/Flying, Steel/Bug, and Fire/Fairy^. That's 22 more species in this group, for a grand total of 92 that resist both of their own types. A far cry from just one that's weak to both of those types.