The Dunfermline MSP, who is refusing to resign despite being convicted of 23 assaults against women going back three decades, has already been removed from Holyrood parliamentary committees and his involvement in proceedings has now stalled for weeks.
But Walker, 71, is still listed as a member of five cross-party groups at the Parliament and moves are under way to expel him from these bodies, which cover aviation, epilepsy, Gaelic, renewable energy, and town centres.
Labour MSP Sarah Boyack, who is convener of the group on renewables, said she had received several representations about Walker's membership of her committee and she was taking advice from officials on how to go about expelling him.
There is no support for the convicted abuser among his Holyrood colleagues, with more than 90 having signed a motion demanding he step down as an MSP. Given the convention that ministers and the Presiding Officer and her deputies do not sign motions, this comes close to unanimity, with only a tiny handful of MSPs arguing it would be more appropriate to await his sentence on September 20 before signing such a motion.
The MSP was expelled by the SNP when he was first charged with domestic abuse and since his conviction on all 23 assault charges against ex-wives and a daughter-in-law he has become a political pariah. This week there was also a protest by Women's Aid activists outside Holyrood.
He has not made a speech at Holyrood since March 1, has not asked a question since July 2, and has not signed a motion since August 1. With his expulsion from the SNP he was removed from committee membership, leaving his only formal point of contact with Holyrood business his membership of the cross-party groups.
The parliamentary authorities have now confirmed the cross-party groups are fully entitled to expel a member. The rules state: "The overall membership profile of the group must be clearly parliamentary in character. Beyond this requirement, any decisions about membership, including whether to limit the number of non-MSP members, is a matter for the group itself."
A Scottish Parliament spokesman said: "The code of conduct makes clear the membership of a cross-party group is a matter for the group itself to determine."
The Scottish Parliament Corporate Body, Holyrood's housekeeping committee, meets today and will consider the implications of Walker's conviction, including any scope to strip him of any pay or allowances.
Lydia Okroj, of Scottish Women's Aid, said: "We would like to see him removed from office so if this is a move in that direction we welcome that. Any indication they take to indicate they do not support his behaviour can only be a positive step."
Walker, from Alloa, Clackmannanshire, was found guilty when he appeared before Sheriff Kathrine Mackie, a specialist dealing in domestic abuse cases and a member of the Government's National Group to Address Violence Against Women.
The pilot specialist court in Edinburgh was deemed such a success it was kept going after the experiment ended.