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Unclear what you're really asking, since you describe switch2 and switch3, but don't describe them. You also don't describe what else is connected to the 6748 line card ports, how busy those other ports might be, what else is in the chassis, whether the 6748 has a DFC, how busy other ports in the other line cards might be, how busy the other switches and their uplinks might be, etc.
In theory, the GigEtherent connection should be able to max out 10 FastEthernet connections.