The current composition of a planet's atmosphere is considered irrelevant to terraforming - though I have seen some super-thick-atmosphered planets within the Goldilocks zone that were not labelled terraformable, so perhaps there is an upper limit, but there is no lower limit. Changing the atmospheric composition, or adding and subtracting atmospheric components, is considered an engineering problem, not a laws-of-physics problem. Just smash a couple of large comets onto an airless planet, for example, and hey presto, instant atmosphere.
The primary criteria for a planet's terraformability are its surface gravity - it must be between 0.4 and 2.0 Earth-standard gravities - and the planet's orbit being within the "Goldilocks zone" of its star system. This is perhaps better expressed as "capable of holding a temperature between 260 K and 320 K, if it were to be given an atmosphere that is breathable by humans". A Human-breathable atmosphere is mostly nitrogen (though argon can be an acceptable substitute) with an oxygen partial pressure within about 10% of Earth-normal, and a total pressure no higher than 4.2 atmospheres. A planet might have a temperature higher than 320 K, or lower than 260 K, and still be considered terraformable, if it is the current atmosphere that is causing the current temperature.
There may be other hidden criteria that occasionally qualify or disqualify a planet unexpectedly (like the example of "super-thick atmosphere" I mentioned above). Moons, for example, are considered to have "extra heat" generated by tidal friction, so terraformable moons are required to be in orbits further out than would otherwise be normal. But for the most part, once you work out where the Goldilocks Zone of a given star system is, any solid planet that falls within the GZ and also matches the surface gravity parameter mentioned above, is almost certain to be terraformable.
The third-party programs like EDD have GZ calculators; they're reasonably accurate, but are much less accurate in multi-star systems, where the algorithms the Stellar Forge uses for adding two Goldilocks zones together are complex and arcane. But in general, a multi-star system will tend to have a wider Goldilocks Zone than a single-star system of the same heat output.
Also note that, although rarely encountered, orbital eccentricity is also considered irrelevant. So long as the median orbital distance (the semimajor axis) is within the GZ, the planet is terraformable - even if the extreme ends of the orbit poke out of the GZ.
This post of mine in the Interesting Orreries thread depicts a planet in a comet-like highly-eccentric orbit within the bubble that is currently being terraformed. The same goes for tidal locking, day length, axial tilt and other orbital parameters that ought to disqualify a planet from habitability.
