There were several valuable worlds above the Truce line available to the Jade Falcons, Steel Vipers, Smoke Jaguars and Nova Cats. However, either the worlds were heavily defended (such as Luthien and Pesht), too deep within enemy territory (meaning that one would either have to seize several other worlds or risk the assigned garrison unit being isolated) was in the wrong direction (not in the direction of Terra) or any combination of the three (such as Coventry which was both deep within enemy territory nor did it lie in the direction of Terra).
The Diamond Sharks were not fully activation to participate in the invasion. They had replace the Steel Vipers as the Reserve Clan once the Vipers and the Nova Cats were activated. Besides, the Sharks had suffered devastating losses on Tukayyid with both participating front-line galaxies being decimated and the single second-line Omega Galaxy cluster being annihilated sacrificing itself at the end to allow the surviving front-line forces to retreat. Soon afterwards two more Omega Galaxy clusters were lost to the Ghost Bears when they reclaimed Nyserta. After such devastating losses the Sharks were in no position to even consider an offensive lest the other Homeworld Clans sense their weakness and try to take advantage.
As for the Vipers or Nova Cats claiming their own invasion corridor, that would offer them no advantage. Not only would it make things easier for their respective rival Clans by creating a buffer zone for them but it would also length their supply lines. To make matters worse, those worlds are likely to be well-defended by units that no longer see the Clans as an unbeatable foe so the fighting for those worlds are likely to be bloody. Not to mention that neither the Jaguars nor the Falcons would sit idly by while their rivals seek to expand their power and influence.
