How often can I use detrending and differencing to make a timeseries stationary?

Question

So I have a lot of timeseries that I check for stationarity by using ADF and KPSS tests. Depending on the results of each test, I can find out if it is stationary, non-stationary, trend stationary or difference stationary. Accordingly I would detrend or difference the timeseries and apply both tests again, to see if the timeseries is now stationary.

Question: If I differenced or detrended a timeseries and the tests show, that the timeseries is still not stationary, can I apply differencing or detrending again? And check again? How often is one allowed to try to convert a timeseries to a stationary process?

These are my methods:

def stationary_test(adf_results, kpss_results):
    if adf_results[1] > 0.05:
        adf_h0 = True
        if kpss_results[1] > 0.05:
            kpss_h0 = True
            stationary_string = 'trend stationary'
        else:
            kpss_h0 = False
            stationary_string = 'non-stationary'
    else:
        adf_h0 = False
        if kpss_results[1] > 0.05:
            kpss_h0 = True
            stationary_string = 'stationary'
        else:
            kpss_h0 = False
            stationary_string = 'difference stationary'
    return adf_h0, kpss_h0, stationary_string


def differencing(df):
    differenced = pd.DataFrame(df[col] - df[col].shift(1))
    return differenced


def detrending(df):
    detrended = signal.detrend(df[col])
    return detrended