load bearing wall with single top plate

Can an existing partition wall with a single top plate be used as a load bearing wall if strengthened? I was considering inserting 2x4 blocking between each stud (studs are 16 o.c.) and nailing them up into the top plate. I would then nail some blocking to each stud (on both sides) to hold up the blocking attached to the top plate - essentially serving as jack studs. Not an ideal situation but would this approach work?
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