Extrapolating from current events, states will soon be fighting over the week after last presidential election so they can hold the first primary of the next election cycle. It's totally nuts, but completely predictable from the incentives: No cost and large perceived benefit from moving one's state's primary forward. What there needs to be is a countervailing cost to moving forward.
Here is the proposal I made 4 years ago: States in the first 25% of primaries (by delegate count) can only award 25% of their delegates on their early primary date, and must hold a second primary three months later to award the rest. States in the next 25% can only award half their delegates at the first primary, and must also hold a second primary to award the rest. Everyone else in the back half can award as normal. So the first half of the primaries only award 18.75% of the delegates. Candidates may get momentum from early state wins, but over three quarters of the delegates will yet be awarded, so later states will matter too.