Let's talk mechanics first. The typical scale is usually just a platform with four load cells used as legs in the corners. The cells are summed up electrically to produce reasonably consistent result regardless of where on a platform you place a weight.
But do you really need four load cells? Not really. You can come up with mechanical arrangement where a single cell doing the measurement. For example something like classic balance scale where counterweight is replaced with load cell. This will save you the cost of three load cells and a combinator, with slightly increased mechanical complexity.
However, the above is irrelevant to the question. I just wanted to give some options to the budget-conscious. From the electrical point, four cells combined is the same as just one cell.
Now, a single HX711 has two inputs, so it can be used to weight two objects [almost] simultaneously. There are two problems with this, however.
First, although SparkFun board does have holes for connecting to channel B, it lacks filtering components for it, so it will be a bit noisier. Second, the gain is different for different channels. For channel A it is either 128 or 64, for channel B it is 32. So, you need to adjust the results accordingly.
Nevertheless, you can use one board for two objects right away. If you need more, plan to have one HX711 per two scales. If you run out of RPi pins your next step would be to use multiplexor to connect several amplifiers to same two pins.
Note, that I am talking about multiplexing digital signals from multiple HX711 to RPi pins, not multiplexing differential analog signal from multiple load cells to a single HX711. While that is also possible the presision will most likely suffer.
The selection of the MUX depends on the number of amplifiers you want to connect. For example, the CD74HC4067 mentioned in comments is fine chip. However it is an overkill if you only want to weight just a few objects. And you need two of these MUXes to do a job.
Much better choice is dual MUX, like ADG725, which can switch DAT and SCK wires simultaneously. You can find other dual chips with different number of channels more suitable for your needs.