No, there's no lower level at Ohio St. The truss isn't actually any deeper than the other ones, really - but it's a deck truss, so no members extend above the bridge deck. The other river bridges are pony trusses, so they appear to be skinnier - the members rise above the bridge deck and the deck visually slices them in half.
If you look closely at the double-deck LSD and Michigan bridges, you'll see that the steel sections are very beefy relative to the distance they span, much moreso than the Ohio and Congress bridges. This is because the double-decker bridges were designed to carry twice the load.
Retrofitting the bridge to carry a lower level would be significant; you'd have to somehow thread a roadway through the bridge anchorages, exactly where the counterweights (solid, thousand-ton concrete blocks) and hinge mechanisms are located. Then you'd have to beef up the bridge members to carry the extra load and remove the diagonal sway bracing that crosses through the space inside the truss.
obligatory cool construction image
fun fact: the bridge leaves are staggered, so when it's raised, the bridge looks like this.
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