Since you mention beta, I assume you're familiar with the capital asset pricing model (CAPM). The concept is that an asset's expected returns are linearly correlated with the market's returns. Of course, there are other ways "normalize" returns, as you put it. We can extend CAPM with Fama-French, which adds market cap and relative value to the equation.
Within the realm of statistical arbitrage, sector-neutrality is very common. Stocks are compared with their sector or industry peers. An added dimension is region or country affiliation, if you were to trade globally.
Then there's arbitrage pricing theory (APT), which defines an asset's price in terms of numerous possible factors. I wouldn't call it "state of the art", but it takes a more realistic view of fair value. You'll need to define your own factors, which you can cull through either fundamental analysis or principal component analysis. You can also buy commercial risk models from numerous vendors. In this case, you may find yourself balancing stocks within the portfolio according to their exposure to things like interest rates or the price of oil.