Hi @Georgina F, 

Not by way of a setting, however you could achieve using a combination of derived rate plans & a minimum stay restriction. Below is an example.

1. Best Available Rate (Base Rate)
2. 3 Night public Rate (derived from BAR with a -20% adjustment) with a 3 night minimum stay restriction

When selecting 1-2 nights, BAR would be visable/bookable.

When selecting 3 or more nights the 3 night rate would be visable/bookable. 

If you keep the rates in the same rate group, only the cheapest rate would be presented in the booking engine.  
You could also make it private and reveal with a voucher if you wanted to

You could also create more with larger discounts, 5 night, 7 night etc.. 

Here are the Mews guides on rates & restrictions 

Hope that helps, let us know if that works for you.

Thank you so much, that is really helpful!