Bear with me... how close would you consider too close in terms of line-breeding? I have a lovely KPWN mare that I am considering breeding next year, as she's stepping down from a career as the perfect ammy horse. She has a terrific brain, and just a few faults that I would like to compensate for: slightly upright pasterns and shoulder that could use more slope. I would also like to improve on her reach as she has a slightly short stride for her size (16.3)
If I were to consider breeding her to Popeye K, for instance, they would share the same great granddam on both dam's sides.
In all honesty, I wouldn't worry about it at all! And that is coming from someone who is very much against doing too much line breeding (inbreeding). People can call it whatever they want...it's called line breeding when it works, it's called inbreeding when it doesn't! But, for your mare and Popeye K to be only sharing one grand dam way back, there is really nothing wrong with that.
i would agree in this case it seems to be far enough back and rings no bells of horses with whom linebreeding has shown to be unsuccessful.
however, it is not a hard and fast rule as it depends and varies from horse to horse.
it has been written up on here before, but for example, in holstein it has been found that 6-7 crosses up relatively close of individuals like corde or ladykiller or cottage son seem only to enhance the desired traits being bred for, while others, like acord ii and contender can give problems with only a single double-up anywhere in a pedigree.
i don't know of any centralised documentation detailing linebreeding findings specifically, but it certainly helps to take time with breeders where high volumes of the relevant breed are produced. they will have had more opportunity than anyone to get a feel for where problems arise, and also where benefits come from the kind of linebreeding you're trying to do.
Now, the mare who went through a recent TB sale who was a granddaughter of both Mr Prospector and Storm Cat on both sides, and was in foal to a Storm Cat son, THAT is too much inbreeding/linebreeding/what ever the heck you want to call it!