PVC to CPVC transition
My understanding is that you can do it if you use CPVC cement - but not ordinary PVC cement.

Here is one reference (from a commercial products supply company) which confirms this:


  Does CPVC to PVC Glue Exist?
  
  ...you cannot use just any PVC cement to join these two materials
  together. CPVC, as we explained earlier, is a stronger version of PVC
  pipe with a higher melting point and tougher chemical structure. This
  means old-fashioned PVC cement will not be fully effective on CPVC.
  
  There is no special “CPVC to PVC glue,” so chemically joining CPVC and
  PVC requires solvent cement and primer that are strong enough to fully
  bond CPVC pipe. 
  
  To connect PVC to a CPVC fitting (or vice versa) follow these steps:
  
  
  Brush CPVC primer on the outside of the pipe and inside of the fitting about 2 inches deep.
  Immediately apply a light layer of CPVC cement to the area that is primed outside the pipe and inside the fitting.
  Slide and twist the pieces together then hold them together firmly for 30 seconds.
  


Also, here is a reference from Weld-On, one manufacturer of (C)PVC cements which also concurs with this advice:


  Q: Will CPVC solvent cement work on a PVC piping installation?
  
  A: Yes. CPVC solvent cement technically will work on PVC piping.
  However, we recommend that the correct ... primer and PVC solvent
  cement for the particular application should be used. Please note that
  PVC solvent cement, because of temperature limitations, is not
  recommended for CPVC piping.




Now, just because it is possible doesn't mean that you should do this. For one thing it might not be to code if you used materials in a way not recommended by their manufacturer. Aside from that, in a critical system (like sewage for instance) you should think carefully if it is worth taking any risk at all.

On the other hand in a nonessential area or in some kind of temporary / emergency circumstance, this might be a reasonable course of action.