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Cantilevers through a solid beam

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I have a design problem where I need to build out the face of a patio from the supporting beams by 16" - and add a parapet above this. The problem is that the total depth of the beam and roof framing is limited to 16 inches - which happens to be the size of the Parallam required for a 24'-0" span. The back-span of the rafters is less than 15 feet and the cantilever is suppose to be, as I mentioned, 16 inches.
 
An idea came to me that I wanted to run by this group.
 
I need to extend at least a 2x4" member over the beam - which is not possible because of the restricted depth. Since this is the compression side of the beam, I thought that I might be able to notch out the 2x4 in the top side of the Parallam (3.5" depth) and extend the 2x4's through the beam. When loaded, the beam will be in compression and the bottom of the rafter is above the neutral axis so that it remains in compression.
I can strap this to compensate for a possible uplift by wind or seismic that might place the upper side of the beam in tension.
 
Any thoughts on this?
Any better suggestions?
 
Thanks,
Dennis Wish PE