Interesting situation. I would expect you would see two transitions in your titration curve. Selecting the correct indicator will depend on the pKa of the weak base. I think your easiest path forward would be to monitor the pH and observe the titration curve. My guess is the quantitative results you're looking for will be pretty clear then. Also, by observing the pH at the equivalence points will help you select appropriate indicators for faster routine analysis in the future.

Thank you Prof. King. I really appreciate of your valuable comment.

You have to test it by titrating a known mixture of bases. Use the color from the test solution as reference when you titrate the unkonwn solution.

I've been thinking about this question for seven months and I think I already have the answer ... I'm joking colleagues! I found out about this question recently, about two or three days. Young Geun Yoo , you raise a case of classical chemical analysis but that does not stop being interesting. After so many months it is very possible that you have already clarified your doubts. But I'm excited about it and I wanted to do some neurobics.

1) The first problem with your question is the indicator you want to use: phenolphthalein. When you titrate an alkali or a mixture of alkalis with a strong acid and phenolphthalein, the pH gradually decreases. The indicator will change from reddish violet (or pink) to colorless. Then detecting the equivalence point of the titration signifies a challenge for the eye, it is easier to detect the appearance of a color than its disappearance. It is better to use an indicator that turns between two colors or that turns from colorless to colorful.

2) Young Geun Yoo, a second topic that arises from your question is that you want to do two titrations (mix and weak acid only) and then get the amount of strong base per subtraction. This necessarily means that the mixture was prepared knowing exactly what volume of the weak acid solution was used although its concentration is not known. This is so?

3) Do not comment on your question if the weak base is monofunctional (acetate or methylamine, for example) or polyfunctional (carbonate, ethylenediamine). Each case raises its own difficulties or advantages.

With a weak bifunctional base, in fact, it would be unnecessary to titrate the solution containing only the weak acid. The whole process could be done only with the mixture but using two indicators and two final points would be obtained: V1 (strong base + weak base first function) and V2 (weak base second function).

If the weak base is monofunctional, the difficulty is to find the appropriate indicator that detects the two bases of the mixture at the same time with the only color turn, obtaining a single end point, V (strong base + weak base).

If the mixture contains a weak monofunctional base, the pH of the equivalence point can be estimated in order to choose the appropriate indicator. I made the calculations to know these pHs assuming different scenarios (see the attached document), in such a way that, the choice can be made according to the case that is presented. As can be seen in the attached document, the highest pH is 7.5. Here Young Geun Yoo comes the fourth problem of the question:

4) Phenolphthalein can not be used in the titration because its approximate turn is from 10 to 8.4. The equivalence point would be anticipated, that is, the point at which both bases are totally neutralized, resulting in a quantification of total bases by default. An indicator that includes the pH of the equivalence point should be chosen. According to the data in the attached document, an indicator that fits all scenarios should have a turn of 7 to 5 although there would be a slight error with extreme cases.