Compact ultra massive array (CUMA) is a new form of the emerging fluid antenna system (FAS) where a huge number of flexible-position antennas are selected to produce the output signal. By making sure that the in-phase channels (similarly for the quadrature channels) of the desired signal at the selected antenna ports align, it builds an advantage of the desired signal over the interference. It is known that CUMA as a multiple access scheme is able to deal with hundreds of users on the same channel use, in the case of rich scattering, if binary phase shift keying (BPSK) is considered. It is nevertheless unclear if higher-level modulation can bring even greater network rate in this extreme massive connectivity scenario. In this letter, we investigate this situation by presenting the average data rate expression of CUMA when M-ary amplitude shift keying (ASK) is used, assuming a binary symmetric channel. Numerical results reveal that M-ary ASK can indeed raise the rate performance considerably.