If you do plant two different pruning groups plant them at either end so that when you prune each one you don't disturb the other. have a read of this before you decide - http://clematisontheweb.org/new-pruning.cfm
hmmm... you have a sun issue there.. you should be made aware that any climber like a clematis, which grows rapidly, will make a beeline for the sun, which happens to be in your neighbours garden, not yours... so unless you are adept at training and cajoling - and I can tell you this takes time and patience.. then much of the flowering will end up on the other side...
You can do it, but it does need to be managed and not left to its own devices... I felt you ought to be made aware of that... it depends how diligent you are as a gardener...
Many thanks for the suggestions and help. Following fairygirls suggestion about taking the bamboo down I have decided against a climber (we live in a rented house and although we plan on staying long term not sure I should dismantle what's been done). Instead will plant some nice taller flowers at the back like calla lilies and allium!
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and read this before you plant a clematis as they have special requirements. Not complicated but getting it right gets them off to a good start - https://www.rhs.org.uk/plants/popular/clematis/growing-guide
You can do it, but it does need to be managed and not left to its own devices... I felt you ought to be made aware of that... it depends how diligent you are as a gardener...