We observe for the first time up to nine transverse modes lasing in the individual elements of a two-dimensional vertical-cavity top surface emitting laser array under pulsed operation, These modes consist of the TEM(0,0), TEM(0,1), TEM(1,0), TEM(1,1), TEM(0,2), TEM(2,0), TEM(1,2), TEM(2,1), and TEM(2,2) modes. Each of these modes couples coherently across the array to form very distinct supermodes. The transverse modes as well as the resulting supermodes are identified by examining the near-field and far-field profiles as well as the corresponding spectra, We also obtain a record 1.4 W (pulsed) of coherent output power from the array during multitransverse-mode operation. In addition, the polarization properties of the array are investigated, It is found that the TEM(0,1) mode is horizontally polarized along the [011] crystalline axis while all the other modes are dominantly vertically polarized along the [011] axis.