Why do you want to increase colour depth? Colour depth has little to do with how intense, or how vibrant the colours look, only with transitions between similar colours.
To put it another way the main consequence of having a low colour depth is the appearance of banding or posterization in smooth colour transitions.
Increasing the colour depth on it's own does nothing to alleviate banding, as 8 bit values like 1010 0111 are simply replaced with 16 bit values like 1010 0111 0000 0000, which is essentially the same number but using more bits.
You can't use interpolation as there's nothing to interpolate between. You could use smoothing but that wont do anything to reduce the appearance of banding as most displays are 8bit devices anyway.
However you can add noise to effectively randomise the low order bits that otherwise get set to zero. And doing so does fight the appearance of banding, which is the only reason I can see to increase the colour depth, hence that's the answer to your question:
Yes, you can increase colour depth, but by adding noise, not interpolating.