The best replacement for modal is modeless.

The best alternatives to modal are rated as following:
★★★★★  modeless
★★★  tonal
★★  model
★★  non modal
★★  push
★★  modeless dialog
★  lightbox
★  rayon
★  viscose
★  popup
★  amodal
★  non-modal
★  push segue
★  tencel
  popover
  mode
  mean
  auxiliary
  tactel
  diatonic

Your alternative for modal is not listed? Suggest!
Speaking about modal, one probably shouldn't forget about tabs bootstrap.

Other search terms related to modal and their ratings are:
★★★★★ tabs bootstrap
★★★ passive voice
cotton
You have in mind a companion for modal and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of modal in all years. Click on graph for more.
modal
modeless
tonal