Yes - it's rather simple.
1) Build a wall - stop any further illegal immigration.
2) Any time an illegal immigrant is stopped by the police, or has any dealings with government officials and is found to be here illegally - send them back home.
Will it be acceptable? To most Americans, yes - to the illegal immigrants, no.
See # 36.
"Any time an illegal immigrant is stopped by the police or has any dealings with government officials and is found to be here illegally - send them back home."