Cope says Parliament's current proportional representation system makes it difficult to hold individual political leaders accountable.
Cope leader Mosiuoa Lekota on Monday said the party had applied to Speaker of the National Assembly Baleka Mbete to have what it calls "a matter of national importance" debated urgently in the House.
The party wants MPs to consider passing a bill on having private individuals voted into the National Assembly and provincial legislatures.
A Private Members Bill has been submitted by the party.
Lekota has, however, slammed the slow pace at which Mbete is moving to have the matter debated, and has now placed his hopes on the matter being discussed once Parliament re-opens in the new year.
"This should be dealt with urgently, so that power should be with the people who vote, and not political parties," Lekota said.
READ: 'Evil' Ramaphosa also broke his oath of office - Cope
Lekota criticised the current electoral system, saying as far as he was concerned, how the Independent Electoral Commission of South Africa (IEC) functions should have been only for the first democratic elections.
"In Codesa, we agreed that the electoral system was to be changed, but it has continued into the fifth democratic government," he added.
Lekota has called on the IEC to advise Parliament on the matter to ensure that it is seen not only as a party issue, but one of national importance.
"Cope will embark on an intensified campaign to solicit the support of civil society, business formations, the religious fraternity... to support the moral call for the return of real power to the hands of the people," he said.
Lekota says political parties have now "monopolised" power away from citizens.
He says the party is confident that there are prospects of success should its motion be debated, and hopes it will be signed into law before the 2019 elections.
Cope's national chairperson Pakes Dikgetsi said there should be a discussion on whether "the country can hold elections fully aware that those elections may be inconsistent with the provisions of the Constitution to allow [individuals] to stand as an independent".
The Constitutional Court earlier this year upheld the individual's right to run for national office, News24 reported in August.
READ: Can independents run for national elections? ConCourt says yes
During a judgment that ruled that citizens had a right to be informed about who is funding political parties, the court also affirmed the right "to stand for public office, and if elected, to hold office".
No order in that regard, however, was made.
Currently, individuals can contest local elections as independent candidates.
A court application was launched earlier this year by former member of the Western Cape legislature Michael Louis and others to have that right extended to provincial and national legislatures.