Based on the tables for double 2x lumber obtained from:
Canadian Wood Council:
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Ground floor building:
One floor, ceiling, attic, and roof building:
Two floors, ceilings, attic, and roof building:
and the load bearing capacities of sawn 4x timbers it would seem
inadvisable to remove the two middle posts.
The maximum loads per lineal foot that can be borne by a 4x6x8 of
various species are found in the table here:
Western Wood Products Association, Technical Note 6, Design Load
Tables for Solid-Sawn Lumber Beams and Headers (869K download):
The above are for new construction. You must also consider that age
and the condition of the timber (prolonged tension, drying, rot,
insect damage, etc.) may affect the bearing capacity of the header.
In addition to the possibility of the failure of the header, you must
also consider that the load formerly shared by four posts will be
divided between the two remaining end posts. This load no longer will
be evenly distributed through the foundation.
The load capacities of posts can be found in these tables:
Western Wood Products Association, Technical Note 9, Design Load
Tables for Wood Columns (Posts):
Software that will help to compute loads and spans:
Western Wood Products Association, Technical Note 8, Timber
Western Wood Products Association, Western Lumber SPAN TABLES for
Floor and Ceiling Joists and Roof Rafters:
American Wood Council:
Tutorial on calculating spans:
Sources for printed tables and manuals:
You might wish to consider installing a steel header and columns and
reinforcing the foundation.
Wood frame construction
Follow the links from the American Wood Council site.