  A family of higher-order rational lumps on non-zero constant background of
Davey-Stewartson (DS) II equation are investigated. These solutions have
multiple peaks whose heights and trajectories are approximately given by
asymptotical analysis. It is found that the heights are time-dependent and for
large time they approach the same constant height value of the first-order
fundamental lump. The resulting trajectories are considered and it is found
that the scattering angle can assume arbitrary values in the interval of
$(\frac{\pi}{2}, \pi)$ which is markedly distinct from the necessary orthogonal
scattering for the higher-order lumps on zero background. Additionally, it is
illustrated that the higher-order lumps containing multi-peaked $n$-lumps can
be regarded as a nonlinear superposition of $n$ first-order ones as
$|t|\rightarrow\infty$.
