Hello;
There are several such telescopes, though they are more commonly known as segmented mirror telescopes. Telescopes like Keck, the Hobby-Ebery Telescope, the clone of Keck being built in the Canary Islands, all have segmented primary mirrors. When properly phased, such a mirror acts much like one large mirror, i.e. the theoretical resolution is as large as if the segmented mirror was a single mirror. This requires that the alignment between the segments be to optical tolerances, i.e. a fraction of a wave. One main drawback of such mirrors, at least for infrared astronomy, is that the emissivity of the mirror is much higher than for a monolithic mirror due to the gaps between the segments. The Large Biinocular Telescope will be an imaging interferometer, i.e. it'll combine the two beams from the two telescopes on the focal plane to get the angular resolution of a larger telescope in one direction at a time.
As far as I know, no amateur has attempted a segmented mirror. For telescopes like Keck, each segment is part of an off axis hyperboloid, and there are 6 different mirror figures among the 36 segments. For HET, the segments are all spherical making a large spherical segmented mirror (with the ensuing spherical aberration). Making a pair of off axis paraboloids isn't easy. For Keck, they used stressed polishing to get the proper figure. An then there's the alignment issue. The mirror support structure must be quite stiff. In the case of Keck, the actuators push on the segments one a second or so, and they need to phase the mirror at least once a night, To do this they have a wavefront sensor and some sophisticated software to automatically align the segments to eachother.
To do this manually, in an amateur telescope, would be challenging to say the least. Typical collimation is much too crude; you'd need much finer control of the mirror alignments. As mentioned above, making several off axis paraboloids isn't easy. It's just as easy to make one large paraboloid in a thin mirror, since off axis paraboloids are typically cut out of such a mirror. One could use several spherical mirrors to make effectively make a larger spherical mirror, but then you'd have to contend with a whole lot os spherical aberration. Even if it could work on paper, it would be impractical as an amateur telescope.
Cheers
Mike Connelley