The systematic changes that could be made are those changes which would make it easier to vote. Political scientists say that people choose to vote when the benefits they get from voting outweigh the costs in time and effort. Therefore, government could potentially increase turnout by lowering the costs of voting.
One thing Texas could do would be to make it easier to register to vote in an election. Today, voters must register at least 30 days before an election. They must either submit an application in person or mail it. They cannot apply online. Reducing this deadline or making it possible to apply to register online would probably increase voter turnout.
Texas could also change its laws about absentee voting or about the hours polls are open. They could keep polls open longer instead of just having them open from 7 AM to 7 PM on election day. They could institute vote by mail systems or give absentee ballots to anyone who asks.
In these ways, Texas could reduce the costs of voting and, potentially, increase turnout.