  As is well known, there are various mass limits for compact stars. For
example, the maximum mass for non-rotating white dwarfs is given by the famous
Chandrasekhar limit about $1.4 M_\odot$ (solar masses). Although the mass limit
for neutron stars is not so clear to date, one of the widely accepted values is
about $2.1 M_\odot\,$. Recently, challenges to these mass limits appeared.
Motivated by the super-Chandrasekhar mass white dwarfs with masses up to $2.4
\sim 2.8 M_\odot\,$, and compact objects (probably neutron stars) in the mass
gap (from $2.5 M_\odot$ or $3 M_\odot$ to $5 M_\odot$) inferred from
gravitational waves detected by LIGO/Virgo in the third observing run (O3), we
reconsider the mass limits for compact stars in the present work. Without
invoking strong magnetic field and/or exotic equation of state (EOS), we try to
increase the mass limits for compact stars in modified gravity theory. In this
work, we propose an inverse chameleon mechanism, and show that the fifth-force
mediated by the scalar field can evade the severe tests on earth, in solar
system and universe, but manifest itself in compact stars such as white dwarfs
and neutron stars. The mass limits for compact stars in the inverse chameleon
mechanism can be easily increased to $3 M_\odot\,$, $5 M_\odot$ or even larger.
We argue that the inverse chameleon mechanism might be constrained by the
observations of exoplanets orbiting compact stars (such as white dwarfs and
neutron stars), and gravitational waves from the last stage of binary compact
star coalescence.
