  Topologically Interlocked Structures (TIS) are structural assemblies that
achieve stability and carrying capacity through the geometric arrangement of
interlocking blocks, relying solely on normal and friction forces for load
transfer. Unlike beam-like TIS, whose deflection never exceeds the height of
the blocks, the deflection of slab-like TIS often does. Yet, the upper limit of
deflection of slab-like TIS, a key parameter defining their loading energy
capacity, remains unexplored. Here, we establish a theoretical upper bound for
the deflection capacity of slab-like TIS and outline a systematic design
strategy to approach this upper bound. This strategy is based on engineering
the contact interfaces such that the non-central blocks are more engaged in the
structural response, leading to a more global and holistic deformation mode
with higher deflections. We demonstrate the application of this strategy in a
numerical case study on a typical slab-like TIS. We show that it leads to a
350$\%$ increase in deflection, yielding a value closer to the upper bound than
previously reported in the literature. We also show that the resulting
deflection mode engages all the blocks equally, avoids localized sliding modes,
and resembles that of monolithic equivalents. Lastly, we show that the strategy
not only maximizes the assembly's deflection capacity but also its loading
energy capacity.
