If you use a big steel plate to join two joists togther in the diagram, I'd expect much of the increase in strength is going to come from the steel, not the added wood.
What's critical is to ensure that you don't have any slippage at the joint between the old wood and the new wood, so I'd opt for a super strong glue rather than mechanical fasteners. I'd just use mechanical fasteners to hold the additional wood or steel to the joist while the clue cures.
And, of course, team up with a consulting engineer or architectural firm to ensure they put their stamp of approval on everything. Your insurance company might not want to cover you if they believe you've done something that affects the structural integrity of your house that wasn't approved by someone officially knowledgable about making such changes.