(...)
#list to store the datasets
datasets.list = list()

#adds first dataset created to the list
observe({
  if(length(datasets.list) < 1 & !is.null(dataset())){
    datasets.list[['dataset()']] = dataset()
  }
})

#renders the UI according to the stored datasets
output$datasets1 <- renderUI({
   radioButtons('datasets', 'Selected dataset:', choices = names(datasets.list[]))
})

#the current dataset the user is working with according to the selection
dataset.current <- reactive ({
   if (length(datasets.list) > 0 & !is.null(dataset())){
      return(datasets.list[[input$datasets]])
   }
})
(...)

#(e.g.) Applying background correction to the current dataset, creating another one
dataset.bg <- reactive({
   input$preprocess
   isolate({
     if (!is.null(dataset()) & input$pMethods == 'bgCor') {
        return (data_correction(dataset.current(),"background"))
     }
   })
})

#Add created dataset to list
observe({
   if(!is.null(dataset.bg())){
      datasets.list[['dataset.bg()']] = dataset.bg()
    }
})