How to modify this tank circuit to obtain a 3rd order passive band pass filter?
You can make a 2nd order low pass or a high pass filter into a 3rd order type but, to try and take a band pass filter from 2nd order to third order would make it asymmetrical in the pass-band. I suspect a 4th order filter would be more appropriate and you can do this (with care or buffering) by cascading two 2nd order BPFs.

So, the 2nd stage follows the first stage and if buffered can be identical in value. If buffering is not used then normally it makes sense to make the loading effect of the 2nd filter on the first filter quite light.

However, if you just want a tighter bandwidth (higher Q) you can increase the series resistor and, to be able to add a load conveniently, you might need a buffer amp on the output.