Using the $e^+e^-$ annihilation data collected above 4.0 GeV with the BESIII detector, we observed the decay $Y(4260)\to\gamma X(3872)$, and found evidence for $X$(3823) in $e^+e^-\to\pi^+\pi^-\chi_{c1}$, and hints of $Y(4140)$ in $e^+e^-\to\gamma \phi J/\psi$. Cross sections for $\ee\to\pp\jp,~\pp h_c,~\pp\psi(2S)$ and $\pi^+D^0D^{*-}$ are measured, and two resonance structures are observed near 4.2 and 4.4 GeV, which can be understood as $Y(4260)$ and $Y(4360)$ states. Charged multiquark states of $\zc(3900)$ and $\zc(4020)$ were observed in $\ee\to\pp\jp,~\pi^+D^0D^{*-}$ and $\ee\to\pp h_c,~ \pi^+D^{0*}D^{*-}$ processes, respectively. Their neutral partners were also observed, thus the isospin vector is established. The spin and parity of $\zc(3900)^\pm$ is determined as $1^+$ to distinguish other hypothesis with statistical significance large than 7$\sigma$.