it's not a matter of how many, but rather of which ones.
the internal design of the keyboard means one key pressed is taking up a "channel", wire, solder path, from the key to the output. cheap keyboards don't have "1 key, 1 path", and they can have as little as 1 path per row of keys.
in addition to this, there is "rollover", a feature which diverts one (or more) signals through a secondary path if the first one is busy.
paths aren't necessarily straight, and they tend to be designed so that the most often used keys are on different paths. add to this a rollover feature (most kbs have 2-kro) and you might be able to press up to 5 or 6 keys at the same time;
however, on the same keyboard, you might not be able to press more than - as little as - 3 keys, if they are specific keys, and the 4th key is also on the same path.
my old dell membrane kb had a problem if i had [W] and [shift] pressed, then the [2] key would not work, but if instead of 2 i pressed for example [3], that one worked.