  We prove that for any countably many one-parameter diagonalizable subgroups
$F_n$ of $\rm{SL}_3(\mathbb{R})$, the set of
$\Lambda\in\rm{SL}_3(\mathbb{R})/\rm{SL}_3(\mathbb{Z})$ such that all the
orbits $F_n\Lambda$ are bounded has full Hausdorff dimension.
