Can I change a 3speed sturmey archer to a derailleur system? Might be daft but can I change an internal hub for a derailleur option. I have an old bike which is slow but I do love it. I want to upgrade my running gear but the "chassis" is still tip-top. I don't want to loose my beloved but am sick of the three speed granddad option. I'm aware that this might not be possible but any help you chaps can offer would be great.
Most three speed internal hub wheels are physically very different in configuration from derailleur (external gear changer) style wheels. Internal hub wheels are fairly symmetrical side to side, but on wheels used on derailleur equipped bikes, the spokes are nearly flat on the gear side and dished on the opposite side. 

To add a rear derailleur, you would need a complete new rear wheel.  There is also the issue of a hanger for the derailleur. Most bikes with internal hubs do not have one. It may be possible to braze one on, but that is complicated.

Adding multiple chainrings in the front is a problem because you still need a chain tensioning mechanism, which is usually done by the rear derailleur mechanism.

Sometimes three speed hubs are added to bikes that are designed for derailleur systems (to multiply the number of gears) but rarely the other way around.

Consider saving the old trustworthy for leisurely rides and investing in a new multispeed bike for more intense activities.