Hoping an LBP or draftsman can help settle this dispute!

We have an old deck / balcony. It is 2m deep and approx 11m long. There are 4 posts that support a single 11m bearer (yes, there is also a stringer along the house). Over many decades the existing bearer (190x45) has sagged pretty bad due to the span between the posts being roughly 3.7m. The joists are in good nick. They are 140x45's and are spaced 400mm apart - I will likely keep these. They are 2m long (hence the 2m wide deck). The posts are approx 1.9m from the house and the joists sit on the stringer at the house end and the bearer at the outside end.

The ten dollar question is; what do I replace the existing, old, sagging bearer with? I know by todays building standard a 3.7m span between posts is not the norm. I don't want to add any more posts, so what can I use as bearer? Steel beam? I-beam? Do I nail a couple of 190x45's together?

I hope my crude diagram helps explain.

Thanks a bunch!