Anything's possible if you know what you're doing because you've done something similar in an identical (or at least VERY similar) situation before and have first-hand knowledge of the actual situation you're looking at. But even then I'd advise getting in a SE to advise, if only because this is a mid-terrace house and you need to cover your ass in the event that anything does go wrong and you need to call on someone else's 'duff-advice-insurance', otherwise known as professional indemnity insurance.

It might be your relative's house, but there isn't a family connection with the neighbours. And I doubt that the family relationship with the person wanting the work done will protect you in the event of any future adverse structural "developments".

You really need to provide pictures of the current situation and at the very least a rough sketch of what's there at present and what you intend should be the outcome. Oh, and explain why you aren't taking out the breast from the remaining two storeys and the roof space (and outside stack), given the consequent need to support all that (considerable) weight.

Just to let you know that old fashioned "Gallows" brackets at high level are now no longer allowed under building regs, any one who tells you other wise, is not telling you the truth..  

most councils now require a steel beam to pick up the front of the breast loadings, followed by concrete lintels and brickwork to pick up the side loadings...

such as...

Usual spot-on post from Wolfie, which highlights the dangers of relying on a google search alone because following your stated intention I've just gone on, out of curiosity because I wasn't aware of the change in the Regs, and YouTube videos abound showing how to fit the very gallows brackets that are no longer allowed.

The following video... http://www.youtube.com/watch?v=bIcuVaVdu10

...was posted on June 22nd this year, 2013.