Dilly has successfully tolerated 6ml/hr and is ready to head to 7mls tomorrow! She's not digesting it very well, it's pretty much shooting right through her, so that's a bit worrisome but at least it will help her liver clear the toxins of the TPN. The fantastic news is that I'm able to breastfeed her twice a day for about 5 mins. I weigh her pre and post feed and am allowed to hold her feed 2 hours and then double the hourly rate in grams (one gram=1ml) that her total feed can be. I subtract the volume she receives in TPN over the nursing time and voila! We're off and running. She's latching like a champ and is quite the protestor when I cut her suckle time short. Definite progress. :)