In a multi-story portal frame, the distribution of moments through the structure is influenced by how forces are distributed across different levels of the frame. The correct answer to the problem statement is: The moments in the lower stories increase, while the upper stories experience lesser moments. Let us understand why this is the case, step by step:

1. Understanding Portal Frames: Portal frames are structures subjected to lateral loads and are designed to endure moments, shear, and axial forces. They are commonly used in multi-story buildings.
2. Effect of Multi-stories: As the number of stories in a portal frame increases, the dispersion of lateral loads due to wind or seismic effects results in varying moment distribution across the frame. This is because the structure has to sustain and transfer these loads effectively to the foundation.
3. Moment Redistribution: In taller structures with more stories, the stiffness of the frame affects how moments are distributed. The lower stories, which are nearer to the fixed base, bear more load transfer, leading to increased moments. Conversely, the upper stories, as they are more flexible, experience lesser moments due to the displacement from the base, guiding much of their loads downward.
4. Justification of the Correct Option: - Lower Stories Increasing Moments: With the increased number of stories, the moment at the base increases due to the accumulated effect of all stories above. - Upper Stories Lesser Moments: Since upper stories displace more freely, they absorb lesser bending moments comparatively.

Thus, when the number of stories in a portal frame is increased, the moment distribution changes such that lower stories take on higher moments than the upper stories. This phenomenon is largely due to the stiffness and load transfer characteristics of the frame's material and the structural integrities involved.