In the current process, all complaints made by a member of the public about a solicitor's service or conduct must be considered by the Law Society council.
The Council of the Law Society of Scotland Bill aims to make it easier for the statutory body to delegate the complaints procedures to committees and sub-committees.
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The changes being debated will allow the Law Society of Scotland to modernise and improve the way it works
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David Preston
Holyrood's Justice 1 Committee has already endorsed the bill, suggesting it would help make the Law Society more "consumer friendly".
The bill was introduced by lawyer and Scottish Conservative Party leader David McLetchie and backed by the other three main parties.
Mr McLetchie said: "The present bill is a significant step forward which will improve the efficiency of the system for dealing with client complaints, be more transparent and increase public confidence in the system."
The Law Society of Scotland said the proposed changes would allow the body to modernise the way it operated.
President David Preston said that as a statutory body, the society was powerless to overhaul aspects of its organisation.
Modernisation
He said: "The membership and functions of the society have grown and consumer expectations have changed.
"It is time for the society's legislative powers to be updated so that the society can continue its programme of modernisation.
"The changes being debated will allow the Law Society of Scotland to modernise and improve the way it works."
Mr McLetchie said the society hoped to bring forward plans for implementing the changes in the coming months.