How can I lengthen my vent stack and are there any negative effects in doing so?
IANAP (I Am Not A Plumber) but I have recently replaced my old cast iron stack.

The relevant part of the International Plumbing Code looks like section 904.  Specifically the following sections may apply to you.


  904.1 Roof extension. All open vent pipes that extend through a roof shall be terminated at least [NUMBER] inches (mm) above the roof,
  except that where a roof is to be used for any purpose other than
  weather protection, the vent extensions shall be run at least 7 feet
  (2134 mm) above the roof.


Note the [number] is usually specified by your local codes as it is very specific to each region.  Some web searching turns up a few forum posts from plumbers in Ontario who say it needs to be 6 inches above the roof.  That does not sound like much to me and if you are already at 6" and having issues it seems reasonable to go higher.


  904.2  Frost closure. Where the 97.5-percent value for outside design temperature is 0°F (-18°C) or less, every vent extension through a
  roof or wall shall be a minimum of 3 inches (76 mm) in diameter. Any
  increase in the size of the vent shall be made inside the structure a
  minimum of 1 foot (305 mm) below the roof or inside the wall.
  
  904.3 Flashings. The juncture of each vent pipe with the roof line shall be made water tight by an approved flashing.
  
  904.7 Extension outside a structure. In climates where the
  97.5-percent value for outside design temperature is less than 0°F (-18°C), vent pipes installed on the exterior of the structure shall
  be protected against freezing by insulation, heat or both.


I don't know the preferred method for doing this but if you plan is to add a coupling from inside the house and "push" the pipe up, I bet you will compromise the water tight seal around the pipe at the roof.  The simplest solution would be to add this extension at the very top so you don't have to mess with the flashing at all.

If this is the main waste/vent stack for the home, I don't think you are allowed to reduce the diameter of the pipe (even up at the "vent" portion).  I don't know if that is still true for smaller vents that service just a few fixtures.

If it is black plastic, it is ABS and should be easy to cut and glue.