He was last seen on Wednesday February 6 that year and his disappearance was declared a Major Crime on Friday June 21, 2019.
Edwin Hinrichsen, 36, and David Young, 39, were arrested yesterday along with a 24-year-old man who cannot be named for legal reasons were arrested yesterday.
Today, they appeared in an Adelaide court but none applied for bail and the trio were remanded in custody.
Their next court appearance is scheduled for September.
Last year, police suggested Mr Purse could have been killed in the suburb of Kilburn around the time of his disappearance.
Police have conducted extensive searches in a range of locations which have failed to find Mr Purse.