Workers Comp Claim & Possible civil lawsuit

I am a paramedic that was recently injured at work in Illinois. I am employed by a private paramedic service, when I arrived on the scene of an emergency ambulance call at a private residence. While exiting the ambulance, I stepped on ice and severly twisted my ankle. I am currently out of work and I have filled a workers comp claim that is following Illinois law. I have received all the medical benefits and the legally mandated 66.667% of my average weekly wage. My question is do I have a claim against the private residence owner? I am and have been in severe pain and I will be out of work for atleast 2 - 3 months and need rehab and possibly surgery. Can I sue the private home owner for any additional compensation to make up for what I am losing while on workers comp?