  Unlike the spin-1/2 fermions, the Lieb and Dice lattices both host
triply-degenerate low-energy excitations. Here, we discuss Moir\'e structures
involving twisted bilayers of these lattices, which are shown to exhibit a
tunable number of isolated flat bands near the Fermi level. These flat bands
remain isolated from the high-energy bands even in the presence of small
higher-order terms and chiral-symmetry-breaking interlayer tunneling. At small
twist angles, thousands of flat bands can be generated to substantially amplify
flat band physics. We demonstrate that these flat bands carry substantial
quantum weight so that upon adding a BCS-type pairing potential, the associated
superfluid weight would also be large, and the critical superconducting
temperature would be tunable. Our study suggests a new pathway for flat-band
engineering based on twisted bilayer Lieb and Dice lattices.
