It is not clear if you have a specific building in mind. The general answer is yes, you can have the same surface area with significantly less volume.
For example, suppose the house was in the form of a parallelpiped (a rectangular prism), with a flat roof. If we include the floor in the surface area we have the volume enclosed is l*w*h, and the surface area is 2(lw+lh+wh).
Let l=60,w=20, and h=10. Then the volume is 12000 cu units and the surface area is 4000 sq units.
If we adjust the length and width so that l=70 and w=16.25, the surface area remains 4000 sq units, but the volume is reduced to 11375 cu units.
The question then becomes, how do you define significantly. We can maintain the same surface area and reduce the volume to virtually zero, but the result is no longer a "house". At some point, if the width is reduced too much it is impossible to live in the home.
A 90x11x10 house has a surface area of 4000 sq units and a volume of 9900 cu units.
A 100x9.09x10 house has an approximate SA of 4000 and an approximate Volume of 9091 cu units.
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