"moving further to" is correct and usable in written English.
You can use it when you are continuing to discuss a particular topic, to show that you are moving onto the next point or idea related to that topic. For example: "Moving further to the issue of the economy, we need to consider how the current policies may affect the trade balance."
The filly responded by moving further to her right, colliding with Special Duty, who maintained a strong challenge but could not quite get past.
But at the next table, Rivi and Yedidya Zuntz, teachers who backed Mr. Netanyahu in 2009, are moving further to the right to support Mr. Bennett.
WASHINGTON — The Obama administration on Thursday issued a new set of proposed rules governing hydraulic fracturing for oil and gas on public lands, moving further to address industry concerns about the costs and reporting burdens of federal regulation.
Surveys show that despite the Conservatives' effort to stamp their brand on Canada, public opinion has been moving further to the left of centre.Proof of this came in the surprising electoral victory of the Liberals in the province of Ontario last June.
But everybody knows he needs a liberal to stop the court from moving further to the right than it already has under John Roberts, the present chief justice, a man more stealth-bomber than aircraft-carrier, whose professions of judicial modesty during his own confirmation hearings in 2005 gave little inkling of the controversial decisions over which he has since presided.
Gesch disagrees and says the debate among biologists is now moving further, to look at how improving nutrition could affect antisocial behaviour.
But as he governed, he moved further to the right.
In the last decade, the Right has moved further to the right and the Left has moved further to the left.
The prime minister, François Fillon, was reappointed, and the French administration moved further to the right.
If it moved further to the periphery, its clout in negotiations would be further reduced.
Were he to become president, they would move further to the centre again.
