If the original header met the header table in the MA code, then it can only support a roof (if that is not the case you have another problem) and the code assumes a tributary loading span of 10 feet (If the span to an unsupported roof ridge is greater than 10 ft you have yet another problem) Assuming the original header was OK, there are three ways to increase it to the larger span.
1) Use a shorter door (if this was a normal slider there are "replacement " sliders that are 2 or more inches shorter) and install three 2x8's since the span exceeds the 8-0 allowed by the code for double 2x8's.
2) Get permission from the building inspector to remove the lower top plate (assuming the upper one is continuous the required distance beyond the jambs) and install three 2x8's if they will fit. The inspector might allow you to trim 1/2" since you are using three members.
3) Use three LVL's cut down to 5 5/8" (or even better 6") if they will fit. Use ones with 2850 psi fiber strength and 2,000,000 psi mod. of elast.(2.0 E) and verify the grade in the field. The manufacturer might provide a stamped design through the supplier if you give them all the relevant loading information. If using their product cut down is an issue for them, you will have to get an independent engineer to stamp it.
Deflection is the issue here. Assuming good lumber, the original two 2x6's just met a deflection limit of L/360 although this is a pretty low standard in my opinion so the original header should have been three 2x6's or two 2x8's.
For the larger span the use of three 2x6's would exceed the L/360 standard by 100%. Two 2x8's barely make it so three 2x8's should be used.
Three 5 5/8" LVL's will meet the L/360 standard but three 6" LVL's would be better.
In what town is the project located?
