In fact, that’s how US laws were intended to work. Federal gives guidelines that apply to all states. The states narrow the scope for any issues that arise.
That's not necessarily true in the US. Federal law can either preempt state law, meaning that states are not permitted to pass stricter or less strict laws in an area (e.g., copyright and patent law), or not, meaning that states are free to pass stricter laws.
Can federal laws prevent state laws from providing privacy protections?