Why Didn't Suleiman the Ist of Rum Attack Rhomania During the Norman Invasion?

After steamrolling his way through Anatolia, with a pause of a few years for consolidation, why did Suleiman ibn Qutalmish, founder of the Sultanate of Rum, go south to conquer Antioch, coming into conflict with his Seljuk kinsmen, ultimately dying at their hands? Why, when Rhomania was being invaded by the Norman Sicilians, did Suleiman not take advantage of this extraordinary opportunity and attempt to finish what he had started?
 

nomisma

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Isn't Suleiman was the close ally of Alexios I? Alexios I supported Suleiman conquering Anatolia, and Suleiman provided troop to Alexios in the war against Norman.

The dead of Suleiman was one of the greatest loss for Alexios I and the Byzantine Empire, which caused the empire finally lost Anatolia (Although byzantine did not formally lost Anatolia until around 1091/92).
 
Isn't Suleiman was the close ally of Alexios I? Alexios I supported Suleiman conquering Anatolia, and Suleiman provided troop to Alexios in the war against Norman.

The dead of Suleiman was one of the greatest loss for Alexios I and the Byzantine Empire, which caused the empire finally lost Anatolia (Although byzantine did not formally lost Anatolia until around 1091/92).
Forgive me if I'm wrong, but didn't Suleiman conquer Anatolia by playing off various emperors and pretenders before Alexios came to power?
 
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