I’m afraid there is quite abit to consider, but here goes.
It is not going to be easy to do this level of high gravity brewing and dilution, and basically I recommend you don’t, at least to the levels you want to. The big boys don’t do it to this extent due to flavour considerations amongst other things. You may get away with a 15 plato wort, but even this may be pushing it for a non automation controlled brewery.
I assume you are producing a beer with an alcohol content around 4.5 %. First may I suggest that you find a beer of about 9 – 10 % alcohol, if you can obtain such a beast. Think about the flavour characteristics. The beer is probably quite rich and fruity, with high levels of esters – grapefruity type nose, more than normal 4 to 5% beers. If you wish to brew at high gravity and dilute, this is likely to be one of the dominant characteristics in flavour / aroma terms.
The main problem with high gravity brewing is the yeast & fermentation. You will almost certainly need higher pitching rates to ferment in a similar time scale. At this high gravity, you are likely to have to aerate the fermenting wort considerably to be able to achieve full attenuation of the wort. In spite of that, you will almost certainly end up with unacceptably high levels of esters after dilution, i.e. it will be a different beer. The aeration may cause fobbing over, and increase losses and hygien problems. The air / oxygen will have to be sterile minimise infection pickup.
The yeast will probably not be reusable for pitching again, and a fresh batch from a normal 11P wort will be required for each batch of high gravity wort. This means you will have to run normal fermentations alongside the high gravity ones. The fermenting wort aeration, if required / used must have its last aeration when the pg is no less than about half original (depends on yeast, fermenting temperatures, wort composition etc.etc.), otherwise you will again get too may unwanted flavoursome by-products produced which carry through to the final beer.
You may need to make the mash thicker to obtain the final gravity you want without boiling the wort to death. If you make the mash thicker, you will have to raise the mashing in temperature slightly to prevent reduction in attenuation limit – this is general, ‘fraid I cannot give any guidelines other than you will probably need to change it by 1 or 2 deg C, but because each brewhouse and raw materials used is different, this is trial and error.
You may need to increase the amount of liquor treatment salts, but possibly not pro rata for the increase in malt loading. This is to ensure that the final liquor mineral ion balance is the same after dilution as before.
You will need to increase the hop rate more than pro rata as high gravity worts, and here I am assuming that you currently boil at approx 12 plato, and would wish / need to boil at 23 / 24 plato. This is because hop utilisation is not as good at high gravity as at lower gravities. If you are looking for a definite hop aroma in your final product, then I suspect that this will not come through particularly well, and you may need to increase “in FV” or “in MV” or “in final pack” dry hopping rates.
The water you use for dilution must be dissolved oxygen free, otherwise you will suffer flavour changes, particularly the production of cardboardy / papery flavours, possibly diacetyl (pear drops), or hazes quite quickly making the beer unsaleable. Dearation with oxygen free CO2 or nitrogen is common. Note the gas must be guaranteed food grade / medical oxygen free.
Having said all that, if you wish to brew at higher gravity, then try for no more than 15 plato in FV, which probably doesn’t get you your capacity increase, but at least all the other aspects indicated above can be controlled reasonably reliably, at least in big breweries. At this gravity, the yeast will be reuseable, and should not require additional aeration, perhaps even using the current aeration rate. You may get away with sufficient aroma from aroma hops in the boil to not worry about dry hopping (which tends to give a different aroma anyway, even when using the same hops). You will probably not have to increase the hop rate by much over pro rata, and should be able to use pretty much the same mash and sparge regime, without major changes to temperatures, stand times, merely reducing the sparge a little and stopping the runoff a little short. You still need to ensure the dilution water is thoroughly dearated and sterile – you don’t want to introduce infection, particularly at this late stage.
Phew. Does this help ?