The Mogi-type true triaxial apparatus (TTA) for rocks provides numerous advantages in terms of complexity, loading capacity, permeability measurement, and cost. However, the spring support design limits the improvements to the loading capacity and stiffness of the vertical frame, which are essential in acquiring the complete stress-strain behavior of relatively large specimens. In this paper, a new TTA achieved by modifying the original Mogi-type design with two moveable frames in a horizontal layout is developed. In addition to the design of stiffer frames with low moving resistance, such a modification provides convenience for experimental operation. Moreover, a positioning device built in the triaxial vessel enables the accurate placing of the specimen. Technical details, including off-center loading, end friction effect, and strain measurement are carefully examined. Calibration and repeatability tests show that the apparatus is stable and reliable. The apparatus is used to conduct tests to examine the influence of intermediate principal stress on the mechanical behaviors of marble. The results demonstrate that, in addition to strength, some other characteristics, including brittleness, fracture angle, volumetric modulus, and stress at the onset of dilatancy of marble also increase initially, but subsequently decrease with an increase of intermediate principal stress. The measurement of the permeability of mudstone during compression reveals that the increase in permeability is closely related to the dilatancy of the mudstone.