Is it possible to reduce body hair density (not totally remove it) with laser treatment?

Most certainly you can reduce the amount of hair rather than getting rid of all of it by simply having fewer treatments than would be necessary to get a complete removal. I would do 2-3 sessions at the appropriate time interval between treatments, and then decide if you're happy with the result, or perhaps you may want another 1-2 treatments to reduce the hair a bit further.

If you initial LHR left you with patch areas, just have your specialist treat these areas.  Trying to achieve your goal can be difficult due to the hair growth cycle. You are probable best off getting 2 appropriately timed treatments and accept the fact that you will likely need to get a fourth and fifth treatment on the areas with heavy growth.  The good news for you is that laser hair removal is really laser hair REDUCTION, as hair always wants to regrow in the areas we are genetically programmed to grow hair.  SO any areas with too much removal will fill in a bit over time.