Conversation so far:
What is Men at Work's Two Hearts?
Colin Hay, Greg Ham and Ron Strykert used session musicians to record their third album, Two Hearts on April 23, 1985.
Which single from Men at Work's album, Two Hearts hit the charts?
Everything I Need was the only the lead single charted in Australia (No. 37) and the US (No. 47) from Men at Work's album Two Hearts
When did Men at Work first break up?
Men at Work first broke up in 1984
Is there addional information about Men at Work's breakup besides when they broke up the first time?
Greg Ham left during the Men at Works's time touring behind the album Two Hearts.
Why did Greg Ham leave Men at Work during their 1984-1986 tour?

Question: What album were they touring for at the time?
Self-contained rewrite: What album were Men at Work touring for during 1984-1986?