How many grants it is possible to have simultaneously? It is feasible to assume that you cannot have more than one grant, since getting a grant means that you are paid for a research project and you cannot work on too many projects at once. So answer should be one. Nevertheless there should be some researchers that have more than one grant. How common is that? Is this field related?
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.