Here's a function to remove the current basemap from the bottom layer, then add a new basemap and move it to the bottom layer.
function setBasemap(basemap) {
if (currentBasemap) {
map.removeLayer(currentBasemap);
}
currentBasemap = basemap;
map.addLayer(basemap);
basemap.bringToBack();
}
var currentBasemap = basemap1; // default map
setBasemap(currentBasemap); // Init
Then add the following within a click event to swap in another basemap:
setBasemap(basemap2);