Curret mirror with discrete BJTs?
It's certainly possible to do this.  In fact, it is done quite often in old test equipment.  However, it can be difficult to get this to work right as the transistor gains have to be very precisely matched.  This is easy to do on a chip as the transistors are physically close to each other and as a result will be built with similar characteristics as well as being thermally connected, but with discrete transistors this is much more difficult.  For one, you will need to make sure that the transistors are at the same temperature by physically connecting the cases together.  Second, you may need to get a box of transistors and swap them out until you find some with similar current gains.