How many grants it is possible to have simultaneously?
At my institution, most researchers have more than one grant.  It is extremely common over a wide range of disciplines, at least in the USA.

Often, one is required to include the "level of effort" in each grant proposal; i.e., the percentage of one's time that will be spent on that project.  That number is never 100%; more often, it may be 10-50%.

In many fields, the "principal investigator" on the grant may do only a small part of the actual research, with the bulk being done by students and post-docs.  This part is very field-dependent.  In some fields, full professors at top universities are expected to have very many grants simultaneously, or at least some very large grants that involve a lot more than the full time of a single person.