There is nothing like the resonance of an open string, our longest string length stopped securely at both ends. In the orchestra, we use many open strings, even for long sustained notes. Not all players tune in exactly the same way, or sometimes excessive humidity or dryness can cause the pitch of open strings to change during performance. Sometimes another section or solo wind player is not in tune with your open string. The pitch of an open string can be influenced by fingering a note or notes on other strings that are in the harmonic series or cancel some unwanted resonance.
With another player, tune your A strings so that they are close, but not exactly in tune with each other. One of you will play the A without any left hand fingers touching, and the other will finger both the A on the G string and the E on the D string while playing the open A. Move these fingers up and/or down until the two open strings blend.
Also experiment with playing the open A while fingering the C on the G string with the A on the D string. This is particularly useful for an A minor, as at the end of the first and last movements of Bottesini’s 2nd Concerto.
For the open D string, try fingering a D on the G string or A string.
For the E string, there are many possibilities, but the most effective may be to finger both the E on the D string, and the B on the G string.
There are some notes that do not ring well on the bass, or cause some confusing sympathetic vibrations.
Probably the most notorious is the low A flat. One of the things which cause the pitch to not be clear on this note is that it causes the A and G strings to vibrate slightly. This is easily remedied by lightly touching both the A and G strings while playing the low A flat. Sometimes further clarity can be brought by fingering the low A flat with the first finger and holding down the A flat on the D string with the fourth finger.
E flat on the D string is improved by dampening the E and A strings. E flat on the A string is improved by dampening the E and D strings. E flat on the G string is helped by dampening all of the other strings.
Low B flats sound clearer when the E string does not vibrate.
A flat on the D string needs the A and G strings dampened.
B flats on D or G string sound better with the A and E strings dampened.
Good luck in your pursuit of pitch clarity and resonance.