The phrase "a further slice of" is correct and usable in written English.
It can be used when referring to an additional portion or segment of something, often in a metaphorical sense.
Example: "In the meeting, we discussed a further slice of the budget allocation for next quarter."
Alternatives: "an additional portion of" or "another segment of".
Close your breasts (no pun intended) and top with a final spread of pesto and a further slice of cheese if you're feeling naughty.
A further slice, of perhaps €15 billion, may come from the IMF.Now Mrs Merkel is under fire both from those who had praised her and from those who now blame her for dragging out the rescue, further destabilising financial markets and raising the ultimate cost of the bail-out.
Forty-eight of these are administered by the Education Department, and a further slice of savings would come from a reduction in agricultural subsidies.
Furthermore, this gentleman already has a monopoly of satellite television and now he is seeking a further slice of the analogue advertising cake.
Osborne's plan to grab a further £75m slice of FOBT profits could push the bookmakers further than just lone staffing their shops.
Ultimately, if Lamont is able to move to the centre and persuades only a further small slice of the more conservative Democrats, Lieberman loses.
Further, a significant slice of the Japanese public still abhors military action.
Some information I received over the weekend from my insurer clearly shows further slicing and dicing of benefits, with costs hiked significantly across the board for all services and drugs, especially those nasty, annoying co-pays.
Further, slicing the fruit body of A. magniverrucata in half will reveal internal structures of cap, gills and stem not present in puffballs.
To honor the orchard further, one might substitute a slice of a diminutive Lady Apple as a garnish.
It is further claimed that a top slice of 8% is being taken by the trusts from the money set aside for schools by the Education Funding Agency – twice the typical 3-5% seen within other chains.
