Clicker trainers give me your opinions please

[HoggleIsMyFriend]

So I've had my dog a few weeks now (1 yo cav) she is a delight. Such a beautiful temperament. I've been doing clicker training with her and she's doing really well. She goes into a down at the possibility of anything yummy.

She had obviously had basic training at her previous home and is quite well mannered. However she has been taught to give a paw and offers this A LOT. I'd really love to see if she could become a PAT dog but putting a paw up is an absolute no no.

Should I attempt to train 4 feet on the floor at all times or to give a paw only on command? Is it possible to get rid of abehaviour that has previously been positively reinforced?
I have a while as she needs to have lived with us for 6 months before we can apply but I'd like to have a plan before I start.

Thanks

Initially I would click for 4 paws on the ground, make that the more rewarding behaviour than a raised paw.

I've just started training lessons with FretPup (clicker training, but that's not relevant to this tip) and one thing our trainer suggested to combat dog's not quite getting it - i.e. going into a down when you've asked for a sit, or lifting the paw without being asked. What she suggested is to say something like 'not quite' and to turn slightly away - i.e turn head and shoulders to the right or the left. Then return and try again - back to being positive and using the clicker and treats to reward the desired behaviour.