Can we make Colpitts Oscillator adjustable?
Say you want a frequency of 1 MHz to 100 MHz - that's 100:1 in range. To do this you'll need two sinewave oscillators and a mixer (balanced modulator).

Set one oscillator to be (say) 300 MHz and the other to vary betweeen 301 MHz and 400 MHz.

"Mix" the two outputs together and you get sum and difference frequencies. Clearly the sum frequencies will be from 601 MHz to 701 MHz but, importantly, the difference frequency will range from 1 MHz to 100 MHz.

Low pass filter the output to largely get rid of the sum frequencies. This filtering process is made easier the higher you choose the individual oscillator frequency range (say) 1.01 GHz to 1.1 GHz.

Both oscillator can be colpitts type in fact they're the one I'd recommend. If you want decent stability of the 1 MHz output be aware that this is quite difficult to achieve given the the stability needed for the oscillators but good luck; I've used this method.