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The observed gravitational-wave background (GWB) spectrum is higher in amplitude than model predictions by a factor of 2─3. Using a semi-analytic model, we evaluate the effect of a high-scatter supermassive black hole (SMBH) scaling relation (M<SUB>BH</SUB>─M<SUB>bulge</SUB>) on models of the nanohertz GWB. By implementing an intrinsic scatter of the M<SUB>BH</SUB>─M<SUB>bulge</SUB> relation, which is larger at higher redshift, but matches local observations, we find that the amplitude of GWB models increases to be consistent with the low-frequency end of the GWB spectrum. This amplitude increase is not uniform across frequencies, a strongly evolving scatter preferentially increases the number density of the most massive SMBHs which, in the GWB spectrum, minimizes the strength of the low-frequency turnover. Our models with positively evolving intrinsic scatter can reproduce the electromagnetically observed overmassive SMBHs at 4 &lt; z &lt; 6 without changing the M<SUB>BH</SUB>─M<SUB>bulge</SUB> normalization though we find that including moderate normalization evolution marginally improves fits to the GWB data. We conclude that the M<SUB>BH</SUB>─M<SUB>bulge</SUB> relation which best describes the available GWB and electromagnetic data sets has intrinsic scatter that evolves as <inline-formula> <mml:math><mml:mi>∊</mml:mi><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>∊</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mo>(</mml:mo><mml:mn>0.56</mml:mn><mml:mo>±</mml:mo><mml:mn>0.4</mml:mn><mml:mo>)</mml:mo><mml:msub><mml:mrow><mml:mi>log</mml:mi></mml:mrow><mml:mrow><mml:mn>10</mml:mn></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:math> </inline-formula> and normalization that evolves as α(z) = α<SUB>0</SUB>(1 + z)<SUP>0.84±0.35</SUP>. The results of this work imply that the M<SUB>BH</SUB>─M<SUB>bulge</SUB> relation we see today is not universal throughout cosmic time and that a diversity of seeding models and growth mechanisms may be at play in the early stages of SMBH─galaxy evolution.