I just did this over Christmas with American Airlines...I called American Airlines Vacations to set it up. The airfare for stopping a few days was only $50 more. We first went to Miami, FL and stayed a few days and went on to Costa Rica. Call the airlines...it won't be apparent online...of course you could patch a SW airlines trip together online with stops that would be cheap but not free

I know United used to offer this. For example, if you were flying through Denver you could do a stop over for a few days and continue on to a different destination.

They also used to offer this if you were flying on miles.

I can't find this anymore. Does anyone know if this is still available?

TIA