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If buff were C, you would have it correct. However, white is not actually a colour. Rather, it is an OFF switch for the plumage colour and pattern genes present in the bird. Meaning that if you add cc to a partridge, it will be white. If you add cc to a blue, it will be white. If you add cc to a buff, it will be white. If you add cc to a lavender, it will be white. If you add cc to a grey, it will be white. Etc.
Since white bred to white will give white without indication of the colours or patterns that are hidden, you could be breeding the white (blue) to the white (partridge) and their offspring to the white (buff) then to the white (grey), then to white (partridge), then to ... You aren't selecting for the hidden genes or the quality of their colour and pattern. So you end up with a jumbled mess of colour and pattern genes. Each bird can and is likely to carry a wide and unique variety of genes. Take away a copy of c and that wide and unique variety is exposed.
Unfortunately, you chose buff for an example--buff is a very complex colour. Something like blue or black or lavender is relatively easy--one gene plus perhaps some helper genes to perfect the colour. Buff, however requires a number of genes, and there are several ways to make buff, which is also a factor in how it mixes with another colour.
In general, silkies are eb/eb. If you start with a buff bird and add even one copy of Pg and you will end up with some penciling, which translates into smutty feathers on a buff. Partridge need red, not the diluted buff, so you don't have a partridge, either. Take away Co and you remove some of the black restriction. Add silver and you dilute the buff, add mahogany and you darken it, add melanizers and you darken any black and may add incomplete lacing, add ... The problem is, you have no idea which of these genes your white bird carries and which it does not. Think of white as a genetic joker--it can be anything.
"If I breed my buff to another bird, what will I get?" That is the same question as "if I breed my buff to a white, what will I get?"
You explained one gene above. Here are punett squares for 2 and 3 genes; the first contains chicken genes, the 2nd does not, but serves to show how each additional gene multiplies the outcome.