Plugged 2" kitchen line

Hi,
I have a 2" line that runs from the kitchen, has about a 4' drop to the basement ceiling and then runs underneath the lower family room (concrete floor) to the end of the house that has the bathrooms & washing machine. All but kitchen work fine. I can access a clean out from the basement right before it goes underneath the family room and it can't be more than a 30' run to the main line. I have run a cleaning machine with a 50' cable and a cutting head through it several times. I hit a few hard spots but get through them and see a little white grease when it is retrieved. It is like it plugs up after I have run through it. I don't get much grease down my drain but is almost like it is a long grease clog that seals back up after I run through it.
Any thoughts??
Thanks
Jerry

The stoppage could be above the point your snaking the line from. If it's not and is as you say a long grease stoppage they do seal back up when you remove the snake. You have to work the h*** out of the cable. Run it a short distance down the line then pull it back. Continue this until you reach the main line. It would also be a big help if you could run some water down the drain while snaking it. This can get pretty messy. Your working with one of the hardest stoppages to clear. Use as large a head on your cable that will fit in the line. C shaped cutter heads work the best.

John