[truncated] In Spring 2007, we observed SgrA* with XMM with a total exposure of ~230ks. We have performed timing and spectral analysis of the new X-ray flares detected during this campaign. To study the range of flare spectral properties, in a consistent manner, we have also reprocessed, using the same analysis procedure and the latest calibration, archived XMM data of previously reported rapid flares. The dust scattering was taken into account during the spectral fitting. We also used Chandra archived observations of the quiescent state of SgrA* for comparison. On April 4, 2007, we observed for the first time within a time interval of ~1/2 day, an enhanced incidence rate of X-ray flaring, with a bright flare followed by three flares of more moderate amplitude. The former event represents the second brightest X-ray flare from Sgr A* on record. This new bright flare exhibits similar light-curve shape (nearly symmetrical), duration (~3ks) and spectral characteristics to the very bright flare observed in October 3, 2002. The measured spectral parameters of the new bright flare, assuming an absorbed power law model taken into account dust scattering effect, are N_H=12.3(+2.1,-1.8)e22 cm-2 and Gamma~2.3+/-0.3 calculated at the 90% c.l. The spectral parameter fits of the sum of the three following moderate flares, while lower, are compatible within the error bars with those of the bright flares. The column density found, for a power-law, during the flares is at least two times higher than the value expected from the (dust) visual extinction toward SgrA* (AV~25 mag). However, our fitting of the SgrA* quiescent spectra obtained with Chandra shows that an excess of column density is already present during the non-flaring phase. The two brightest X-ray flares observed so far from SgrA* exhibited similar soft spectra.