How repeated doses settle to a plateau
When a drug is given repeatedly at a fixed interval, each dose adds to whatever remains from earlier doses while the body continues to clear the drug. Early on, intake outpaces elimination and the average concentration climbs. As the level rises, the amount cleared per interval increases until it equals the amount being added. At that balance point the concentration oscillates around a stable average, which is steady state.
A useful rule of thumb is that reaching steady state takes about five half-lives, regardless of the dose size or how often it is given.
What changes the plateau and how to reach it sooner
The height of the plateau depends on the dose, the dosing interval, and the body's clearance, while the time to reach it depends only on the half-life. A loading dose does not change the eventual steady-state level; it simply jumps the body to that level faster so the drug works sooner.
Because longer half-lives mean slower equilibration, dose changes for such drugs take time to show their full effect. This is general educational information, not medical advice; dosing schedules should be set by a qualified prescriber.