In this paper, we discuss investment allocation to multiple alpha streams that are traded on the same execution platform. This includes when trades are crossed internally, resulting in turnover reduction. We discuss approaches to alpha weight optimization, in which profit and loss is maximized subject to bounds on volatility (or the Sharpe ratio). The presence of negative alpha weights, which are allowed when alpha streams are traded on the same execution platform, complicates the optimization problem. By using a factor-model approach to the alpha covariance matrix, the original optimization problem can be viewed as a one-dimensional root-searching problem plus an optimization problem that requires a finite number of iterations. We discuss this approach without costs, with linear costs and with nonlinear costs in a certain approximation. This makes the allocation problem tractable without forgoing nonlinear portfolio capacity bound effects.