If reports are to be believed, the the new Instagram app version 7.12.0 on Android might begin supporting multiple accounts on one device. This is the first time, since its inception, that Instagram has even thought of the possibility of multiple accounts.
However, not everyone who downloads the newest version of the app will receive this feature as it is still being rolled out in stages. Additionally, Instagram has not made any official statement yet. In case you did receive the update, then you should see an “Add Account” option under the “Clear Search [...]