i believe trivially in material reincarnation, i.e. the matter we are composed of tranfers to new and other living entities in due time. to the extent consciousness supervenes on matter it can be said something of our "souls" is preserved and absorbed by new life as well.

also i think people are more than individuals and live on in their legacy. much like going to sleep ends consciousness but not life, so too does death end life but not our legacy. in this sense that which in us identifies with the legacy instead of with the individual lives on after death.