Do you have Relays with overlapping contacts?

Yes, there is G2A-4L32A General-purpose Relays. OMRON calls "overlapping contacts" "MBB (Make Before Break) contacts". (Specify the coil voltage after the model number.)

MBB Contacts (G2A-4L32A)

"MBB contacts" is an abbreviation for Make Before Break contacts. Relays with MBB contacts have an overlapping mechanism where the NO contacts close before the NC contacts open. These are also called "continuous contacts."