Increasing the current will only affect the torque being produced at lower speeds and should not affect the top speed, as the current being drawn at full throttle will automatically reduce as the motor's speed increases.
Motors run very inefficiently when drawing high current at low rpm, and a large portion of the energy being supplied to the motor is simply converted into heat.
If an internal controller becomes too hot due to sustained high load at low speed, it will eventually cut out completely to prevent further heat being generated and will only start working again when the temperature of the controller drops back down to a safe level again.
I don't think you would damage anything by increasing the current of an internal controller, but I won't guarantee it.
However, with an external controller, there would be no temperature protection whatsoever for the motor, and I suspect that the insulation on the stator windings could be permanently damaged if the motor overheated due to being constantly overloaded.
If you want to increase your maximum speed
(and the controller is already set for maximum rpm) you will need to upgrade to a higher voltage battery
and a throttle control to match.
However, if you're already using a 48V battery, you would also need to use a higher voltage external controller as well.
Alan