Thanks for the great question. Finding information on all the storms that have been active at one time in different oceans around the world is not an easy feat, so hopefully this information about the Atlantic and the Pacific Ocean will help to answer your question.

In recent history there have been as many as 4 hurricanes in the Atlantic Ocean at one time, the last time happening September 25-27, 1998 with Hurricane Georges, Ivan, Jeanne, and Karl. A climate modeler has guessed that there is potential for a maximum of seven hurricanes in the Atlantic at once, but this is very unlikely because there just isn't enough space for them all in the ocean.

This number is not counting cyclones (hurricanes that form in the South Pacific and Indian Oceans) or typhoons (hurricanes that form in the Northwest Pacific Ocean, near Japan). There have been as many as eight tropical cyclones (storms that are slightly weaker than hurricanes) active at once in the Pacific Ocean, as recently as last July!

The largest number of hurricanes present at once (on record) is 4, having occurred in both 1998 and 1893.

An estimate for the maximum possible is 7, though this could change as climate changes. The largest number of hurricanes in a single year is 15, which occurred in 2005 (Reference: first link above).

The answer seems to be about four, due to the size of the Atlantic ocean. Presumably there could be more in the Pacific and Indian oceans, though.

Popular Mechanics has an article about how many hurricanes there can be at the same time. It says: "Right now there are three, but what's the upper limit?
link here .
The article was posted Sept. 10, 2018. That's just hurricanes in the Atlantic Ocean. There are also hurricanes in the Pacific Ocean.

Here's more from Popular Mechanics: "By the time you get to four or more cyclones at one, that level is found in only about 340 records—less than one percent. At about four simultaneous storms, Gnanadesikan says, "you might start running out of seeds." ..."I'd guess that seven might be the maximum possible," Gnanadesikan says."