Jon also wants his support lowered. Supposedly it's set at over $20,000 a month. No mention if he does or doesn't pay it, just the amount. It's also said he's living with his brother and he says the divorce agreement says he can live in the house when Kate is gone and the guest house when she is there, but I guess she hasn't allowed that. At least that is what his side is.
My guess is, if the support goes away or gets lowered considerably, his lawsuit for physical custody and the right to live in the house may too.