Are overlapping generation (OLG) models extensions of a DSGE model? Are overlapping generation models (OLG) extensions of a dynamic stochastic general equilibrium (DSGE) model? Or aren't these DSGE per se?
You can find OLG models that do not classify as DSGE (in particular, the model might not be stochastic) as well as DSGE with overlapping generations (contrary to those with infinitely lived agents). 

You can find more detail on this on this working paper by Assous and Duarte (2017), as they note 


  In the early 1980s, when the real business cycle macroeconomists
  brought one single model (a perfectly competitive growth model with
  infinite-lived agents, flexible prices, and perfect information) to
  bear on any macroeconomic issue, several macroeconomists were working
  with OLG models and addressing business fluctuations matters. Besides
  the efficiency issue, the model seemed to have much more to offer. New
  classical economists such as Wallace and Lucas saw in the OLG model
  the possibility to develop new microfounded models of fiat money
  without postulating that money balances enter the utility function of
  agents. At about the same time, other macroeconomists discovered that
  OLG models give room for either deterministic or stochastic
  oscillatory trajectories. Endogenous cycles and chaos as well as
  sunspot equilibria were then shown to occur in the presence of
  perfectly competitive product market devoid of any nominal price
  rigidities. Gradually over time, important contributors to that
  literature — most notably, for our interests here, is Woodford —
  strove to transfer OLG conclusions to infinite-lived agents models. In
  this context, new dynamic models with market imperfections were
  developed, initially with flexible prices, that eventually became the
  hallmark of the sticky price, DSGE macroeconomics (earlier referred to
  as the new neoclassical synthesis).