You can apply a different mode as often as you like, on either app, on any plan.
How
On the web
On the phone
What changes
Your recommendations are rebuilt with the new mode's targets and foods-to-limit list. The previous set is replaced. Any mode-specific screen on the phone changes to the new mode's.
What is kept
What each app remembers
The phone remembers the mode you last applied on the phone and shows it as Current Mode. The web shows the mode your newest recommendations were built with. Because both apps rebuild the same recommendations, they agree once you have applied a mode on either; a mode applied only on the web shows on the phone's Current Mode after you apply it there too.
If it fails
If the rebuild fails on the phone, the mode is kept on the phone and a message says so; tap the mode again to retry. On the web the button shows Failed to apply mode and you can click it again.
One mode at a time
Modes do not combine. If you have a kidney stone history and high blood pressure, for example, apply one mode and rely on your health conditions for the rest: the conditions on your profile shape your recommendations whichever mode is applied.