Both bipolar transistors and FETs are proportional devices.
The collector current in a bipolar transistor will be the base current * the gain (hFE) of the device.
(The hFE is given in the data, for a typical collector current. It tends to fall at high currents).
If that level of current is great enough to apply close to the full supply voltage across the load, the transistor will "saturate", so more base current will have little to no effect.
eg. If a transistor had a gain of 10 at 100mA, operating on a 10V circuit with a 100 Ohm collector load:
With 5mA base current, the collector current would be around 50mA, so about 5V across the load resistor and 5V between emitter and collector.
For switching applications, such as in switched-mode PSUs or logic, using anything up to 10x more base current is not uncommon, to ensure the lowest voltage drop across the transistor while it is conducting - though a saturated transistor switches off slower than one operated in its linear range.