  We present a modification of the Rose-Machta algorithm (Phys. Rev. E 100
(2019) 063304) and estimate the density of states for a two-dimensional
Blume-Capel model, simulating $10^5$ replicas in parallel for each set of
parameters. We perform a finite-size analysis of the specific heat and Binder
cumulant, determine the critical temperature along the critical line, and
evaluate the critical exponents. The results obtained are in good agreement
with those obtained previously using various methods -- Markov Chain Monte
Carlo simulation, Wang-Landau simulation, transfer matrix, and series
expansion. The simulation results clearly illustrate the typical behavior of
specific heat along the critical lines and through the tricritical point.
