  The $S=1/2$ square-lattice $J$-$Q$ model hosts a deconfined quantum phase
transition between antiferromagnetic and dimerized (valence-bond solid) ground
states. We here study two deformations of this model -- a term projecting
staggered singlets as well as a modulation of the $J$ terms forming alternating
"staircases" of strong and weak couplings. The first deformation preserves all
lattice symmetries. Using quantum Monte Carlo simulations, we show that it
nevertheless introduces a second relevant field, likely by producing
topological defects. The second deformation induces helical valence-bond order.
Thus, we identify the deconfined quantum critical point as a multicritical
Lifshitz point -- the end point of the helical phase and also the end point of
a line of first-order transitions. The helical-antiferromagnetic transitions
form a line of generic deconfined quantum-critical points. These findings
extend the scope of deconfined quantum criticality and resolve a previously
inconsistent critical-exponent bound from the conformal-bootstrap method.
