100% it is possible; You would need the following to happen :
1. The war in Bulgaria was pretty much over by 1014 (Battle of Kleidion). From there till 1018 it was minor mop up situations.
2. Per Treadwell the Byz army exceeded 250,000 and might have numbered 325,000, Many of these of these troops were out of condition and Basil had made the decision to keep paying them vs them going into rebellion.
3. In 1025 Basil had decided to conquer Sicily, then he died pre the invasion. The Byzantines liked land, and to the east their was little valuable land, unless he went south. He also did not want to strengthen the hands of the eastern nobility which had fought 2 civil wars against him. So valuable land would be Sicily, and middle and northern Italy.
4. Have him decide in 1015 to invade Sicily with a force of 20,000 Tagmatic Mercs. troops, in addition call up the poorly trained Thematic interior forces (80,000 over 5 years) as part of the invasion force. Capture Sicily, and it would most likely go like the invasion of 1030, and fall in 2 years. Transfer the Thematic forces and train them up to standards. By 1017 i could see the profits and success would point towards a capture of some of the Lombard kingdoms as well as Rome. I think once you started north then the natural defensive lines would be to conquer up to the Alps.
5. In the time frame from 1015 - 1035 really no force in the world could have defeated the Byz. If you have a force of retrained (80,000) Thematic troops and a good size Tagmatic forces you would then have a stable troops.
The extra income form the capture of these areas would have created a self financing area, and most likely provide a positive cash flow for the future. Now you need to have George Maniakes not die after he was winning the battle against Constantine in 1043, and then you have a strong emperor in place.