  The sensitivity of continuous gravitational-wave (CW) searches for unknown
neutron stars (NSs) is limited by their parameter space breadth. To fit within
reasonable computing budgets, hierarchical schemes are used to identify
interesting candidates using affordable methods. The resulting sensitivity
critically depends on the number of candidates selected to follow-up. In this
work, we present a novel framework to evaluate the effectiveness of stochastic
CW follow-ups. Our results in realistic datasets allow for a ten-fold reduction
of the computing cost of pyfstat, a well-established follow-up method. We also
simplify the setup of multi-stage follow-ups by removing the need for
parameter-space metrics. The study was conducted on Gaussian and real O3
Advanced LIGO data using realistic durations, and covered both isolated and
binary sources. These results will have a positive impact on the sensitivity of
all-sky searches in the forthcoming observing runs of the LIGO-Virgo-KAGRA
collaboration.
