  We propose and analyze a family of periodic braiding protocols in systems
with multiple localized Majorana modes ($\textit{majoranas}$) for the purposes
of Hamiltonian engineering. The protocols rely on double
braids$-\textit{draids}-$which flip the signs of both majoranas, as one is
taken all the way around the other. Rapid draiding dynamically suppresses some
or all inter-majorana couplings. Protocols suppressing all couplings can
drastically reduce residual dynamics within the nearly degenerate many-body
subspace ("majorana purification") producing more robust computational
subspace. Non-trivial topological models can be achieved by selectively
applying draids to some of overlapping (imperfect) majoranas. Importantly,
draids can be implemented without having to physically braid majoranas or using
projective measurements. In particular, draids can be performed by periodically
modulating the coupling between a quantum dot and topological superconducting
wire to dynamically suppress the hybridization of majoranas by more than an
order of magnitude in current experimental setups.
