Yes, it is definitely possible. One possibility is to run fumigation which means that the LPG is injected into the inlet air. The diesel injection quantity should then be reduced to a small pilot quantity whose purpose is to ignite the LPG/air mixture. Another possibility is of course to mix LPG and diesel and inject the mixture directly into the cylinder but this is more complicated due to lubricity issues.
yes it can be done, not only with LPG but even with CNG also BUT it doesn't have any significance and economic perspective due to following issues -
1. By adding LPG, compression ratio has to be decreased that is impractical because than it wont be no longer CI engine.
2. Spark plug has to be introduced to ignite LPG.
3. Crankshaft, connecting rod etc. have been made for low rpm in diesel engine but with the use of duel fuel technology they have to be run on high rpm. so all these components will be stressed more causes wear and tear.
4. Due to high compression ratio of diesel engine when LPG is mixed, knocking will occur causes no longer quieter operation.
5. Even it wont give significant economic justification as fuel saving due to above consequences.
With all these disadvantages you can avoid harmful emissions such as particulates, CO etc with diesel/LPG mixture