This work presents GaussStones, a system of shielded magnetic tangibles design for supporting multi-token interactions on portable displays. Unlike prior works in sensing magnetic tangibles on portable displays, the proposed tangible design applies magnetic shielding by using an inexpensive galvanized steel case, which eliminates interference between magnetic tangibles. An analog Hall-sensor grid can recognize the identity of each shielded magnetic unit since each unit generates a magnetic field with a specific intensity distribution and/or polarization. Combining multiple units as a knob further allows for resolving additional identities and their orientations. Enabling these features improves support for applications involving multiple tokens. Thus, using prevalent portable displays provides generic platforms for tangible interaction design.