I don't have a 14 way divided bag but as far as I know, the bag can hold the oversized grip.

I had no trouble getting in a Super Stroke Mid-Slim 2.0 into my Titleist 14 way carry bag.  I would think one even larger than mine would also fit with no trouble.

Stand bag or cart bag? I have both a 2012 and the new 2014 Titleist Lightweight Cart Bag with 14-way dividers, as well as a Lightweight stand bag, also with 14-way dividers. The cart bags have large putter openings. The stand bag has the same size opening as the other 13 openings. I don't use an oversized putter grip, but I am sure one would fit in either of the cart bags, though the  older version (2012 model) is not quite as big as the newest (2014) model. As far as the stand bag goes, I'm confident an oversize grip will fit with no problem, though it might require a touch more effort to get in and out as easily. 

Yes, I have mid size grips and the fit no problem.  

I have the 14 way premium stand bag and my oversized grip will only fit in the top dividers. The ones I normally use for my woods.

I have a Titleist 14-way premium stand/carry bag and have had no trouble getting a putter with a Super Stroke Mid-Slim 2.0 grip in and out.  

Yes with no problems!!

I have a Titleist cart bag with the 14 way it has the separate putter hole and my super stroke fits fine. The only issue is when you pull it out sometimes it gets hung up. If you pull it straight up and out it happens allot less

Thanks guys!