welcome to teachat!
Usually I don't mix brews in the chahai. This is for two reasons:
- I don't have to concentrate on two things at once (serving & brewing)
- I don't mix the flavors of two different brews
However I will use the chahai to mix brews if I am using a small vessel to serve a large number of people, which I have done on a couple occasions.
You will get a better experience out of gongfu style if you focus on only one thing at a time and if you focus on the flavors of each individual brew.
But if you are serving many people or have another reason to mix a large number of small brews into a large volume (maybe you want to fill a thermos to take to work), then a large chahai is a good purchase.
edit: are you steeping the leaves while you drinking from the first chahai? This is what I assumed you were doing when I wrote the preceding post. However if you are not steeping the leaves and your second brew still turns out bitter, shorten the second steep. Often I find that the first one or two brews need to be longer than the next ones because the leaves need time to open up and awaken (This is especially true with Japanese sencha for whatever reason, although I'm aware we're discussing Chinese style tea). So for instance I might brew 30sec, then 10s, 15, 20, 30, ... until I'm done. However the likelihood that I need to shorten the second or third steep is much lower if I rinse the tea with hot water before the first brew, as this can open and awaken the tea as well. Different teas need different amounts of time to awaken. Balled-up oolongs take especially long, and so does highly-compressed pu'er, whereas with wiry yancha or dancong I usually don't need to do a shorter steep than the first.