The seven basic quantities are selected to allow other quantities to be defined in terms of these measures. It is possible to have 8 or more, but then they would not be independent and at least one could be derived from the others.
Some people argue that even the seven are not independent since distance and time are related by c, the speed of light which is a fundamental constant (under defined conditions). Therefore metre or second can be eliminated as a basic quantity by defining metre = c*time or second = metre/c. However, I contend that this is simply replacing distance and time by either speed and time or by speed and distance so that the number of basic quantities does not change.
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