This is related to pump head , not pump size. Pump head is the ability of the pump to push the water up and overcome water gravity while flow is the capaicty to push a mass of water in one period of time. When you need high flow because your shower have a lot of nozzles / outlet , it is not possible to have a pump which have pump head only 2.8 bar to overcome height of the third floor ( I think it should be not less than 10 m. above ground level which equal to pump head = 1 bar ) , over come friction loss in small diameter pipe ( higher flow , higher friction ) and still have remaining pressure to give you high velocity spray at your shower.
It is for sure that your discharge pressure at 2.8 bar measured at outlet of your pump is not enough. Your pump may be designed to be used for house that have only second floor. Nothing wrong with the pump , it was the matter of purchasing without knowledge and wrong or no suggestion from vendor.
I recommend you to consult with your pump supplier to find out if your pump can be adjusted to discharge at 3.5 to 4 bar instead of 2.8 bar.
I am afraid that you buy a wrong pump and the worst case is you may have to change pump to get higher head ( more outlet pressure ) , Ebara pump as recommended in comment #19 should be O.K.
Normally , pump head can be read at its nameplate . 1 bar = 100,000 Pa or 100 Kpa and equal to 14.7 Psig.
If name plate showing 4 bar which equal to 400 Kpa or 59 Psig or 40 Kg/cm2 , that should be O.K.
26 พ.ย. 49 14:21:59
A:126.96.36.199 X: TicketID:132728