Type II Kardashev Civilisation — A civilisation that is able to harness all of the power available from a single star, approximately 1026 W. Again, this figure is variable; the Sun outputs approximately 3.86×1026 W. Kardashev's original definition was 4×1026 W.
Stellar Propulsion system, utilising a gigantic statite mirror/solar sail. The resulting radiation pressure differential would propel the whole star, albeit with a minute acceleration. Such a system would easily be stable for millenia.
It has been calculated that all such stellar engines would emit a large proportion of infra red radiation. One star system known to emit a higher than expected level of IR is the Sirius system. Whether such megascale structures would be plausible in a binary system is unknown.
A megastructure designed to completely enclose a star for the purposes of energy collection of habitation spaces.
A Dyson sphere considing of a solid shell, completely encapsulating a star. Considered implausible because of the difficulties involved (including the material stresses exerted on such an object).
A more plausible variant on the Dyson sphere, consisting of a vast array of smaller satellites orbiting a star in a dense formation. One proposed structure is one or more rings encircling the star at a fixed orbital distance.
A megastructure based on the dyson sphere, capable of immense computational capacity. Such a structure would consist of a number of nested Dyson spheres constructed around a star. Each shell would consist primarily of nanoscale computers, designed to operate at the temperature of each respective sphere, and re-emitting energy at a lower frequency.
The extraction of useful materials from a star. Effectively solar mining.
Any combination of class A and B stellar engines.