Dishes CAN be extended but, unless the dish was already designed with extension in mind, you will find it difficult. Extension usually only applies to centre feed (prime focus) dishes, not off-set types.
All dishes are shaped in profile as a parabola so extending the parabola shape will extend the dish. Extending a 1.2m dish to, say, 1.5m is not likely to give as much of a gain as simply buying a 1.5m dish as you will be altering the f/d ratio compared to a repalcement 1.5m dish. In order to get the best of an enlarged dish you will therefore need to alter the LNB and, unless it has adjustable scalar rings, you will be unable to utilise most, or even any, gain. What you WILL get by extending a dish is a greater rejection of unwanted off-centre signals so you might notice a difference because of this.