If you want to have the effect of reusing a stream, you might wrap the stream expression in a Supplier and call myStreamSupplier.get() whenever you want a fresh one. For example:
Supplier<Stream<String>> sup = () -> someList.stream();
List<String> nonEmptyStrings = sup.get().filter(s -> !s.isEmpty()).collect(Collectors.toList());
Set<String> uniqueStrings = sup.get().collect(Collectors.toSet());