  In this work, we calculate the higher mass spectra for the $2S$- and
$1D$-wave fully-charmed and fully-bottom tetraquark states in a nonrelativistic
potential quark model. The $2S$-wave fully-charmed/bottom tetraquark states lie
in the mass range of $\sim (6.9,7.1)$/$(19.7,19.9)$ GeV, apart for the highest
$0^{++}$ state $T_{(cc\bar{c}\bar{c})0^{++}}(7185)$/
$T_{(bb\bar{b}\bar{b})0^{++}}(19976)$. Most of the $2S$-wave states highly
overlap with the high-lying $1P$-wave states. The masses for the $1D$-wave
fully-charmed/bottom tetraquarks are predicted to be in the range of $\sim
(6.7,7.2)/(19.5,20.0)$ GeV. The mass range for the $D$-wave tetraquark states
cover most of the mass range of the $P$-wave states and the whole mass range of
the $2S$-wave states. The narrow structure $X(6900)$ recently observed at LHCb
in the di-$J/\psi$ invariant mass spectrum may be caused by the $1P$-, or
$2S$-, or $1D$-wave $T_{cc\bar{c}\bar{c}}$ states. The vague structure
$X(7200)$ may be caused by the highest $2S$-wave state
$T_{(cc\bar{c}\bar{c})0^{++}}(7185)$, two low-lying $3S$-wave states
$T_{(cc\bar{c}\bar{c})0^{++}}(7240)$ and $T_{(cc\bar{c}\bar{c})2^{++}}(7248)$,
and/or the high-lying $1D$-wave states with masses around 7.2 GeV and
$J^{PC}=0^{++},1^{++},2^{++},3^{++}$, or $4^{++}$. While it is apparent that
the potential quark model calculations predict more states than the structures
observed in the di-$J/\psi$ invariant mass spectrum, our calculations will help
further understanding of the properties of these fully-heavy tetraquark states
in their strong and magnetic interactions with open channels based on explicit
quark model wave functions.
