What is the leading alternative to the "stages" model of grieving?
According to "Theories of Grief and Bereavement" by Boerner et al. (2015) the leading theories are:


The Four Component Model from Bonanno and Kaltman


Context in which loss occurs 
Subject meanings associated with loss
Changes in representation of the lost loved ones over time
Presence of coping and emotion processes

The Dual Process Model from Stroebe and Schut


Loss-oriented coping
Restoration-oriented coping



The article also notes that further work needs to be done in terms of:


Effects of inter-personal relations
Influences of cultural background
Biological aspects