  We investigate secular evolution in hierarchical quadruple systems as a
formation channel of mass-gap black holes (with masses of about $3-5$
$M_{\odot}$) in systems that will eventually lead to binary black hole mergers
detectable by ground-based gravitational wave detectors (LIGO/Virgo). We show
that in a 3+1 hierarchical system, two episodes of induced mergers would first
cause two neutron stars to merge and form a mass-gap black hole, which will
subsequently merge with another (more massive) black hole through a second
induced merger. We demonstrate that such systems are stable to flybys, and
their formation would predict a high mass ratio and eccentric merger of a
mass-gap black hole with a more massive black hole companion. Such a formation
channel may explain observed gravitational wave events such as the
recently-discovered LIGO/Virgo events S190814bv and S190924h.
