  In 1985, Leggett and Garg formulated a class of inequalities for testing the
compatibility between macrorealism and quantum mechanics. In this paper, we
point out that based on the same assumptions of macrorealism that are used in
the derivation of Leggett-Garg inequalities (LGIs) , there is a scope of
formulating another class of inequalities different from standard LGIs. By
considering the three-time measurement scenario in a dichotomic system, we
first propose an interesting variant of standard LGIs and show that its quantum
violation is larger than the standard LGI. By extending this formulation to
$n$-time measurement scenario, we found that the quantum violations of variants
of LGIs for a \emph{qubit} system increase with $n$, and for a sufficiently
large $n$ algebraic maximum can be reached. Further, we compare the quantum
violations of our formulated LGIs with the standard LGIs and no-signaling in
time formulation of macrorealism.
