can you increase satellite internet upload speed by adding more dishes?

if a single dish provides a certain, relatively low upload speed, does this mean that we can just add extra dishes nearby and hence increase the upload speed multiple times? Presumably in this hypothetical case the added cost of the extra accounts would be worth it.

Perhaps a related question is, how does the satellite multiplex its transmission between the various dishes it is servicing to make sure that each one gets the data intended for it?

Not sure about your first question, but according to the internet the dominant technology is Time Division Mutiple Access in which each customer is granted a very small time interval to which data is served in frequent bursts.

it seems to me that this time division multiplexing implies that upload speed could actually be arbitrarily increased for a single dish just by permitting it to fire its bursts more often (at the expense of some other dishes), let’s say for extra fee. Are such things already done? Or is my supposition incorrect?

Probably, but I imagine the satellite operator dynamically allocates time shares based on current traffic conditions anyway (5 users are uploading, each gets 20%, 10 users each gets 10% etc). Broadcast power with probably be a more limiting factor, but I’m not an expert. I would think a bigger dish would be a more effective way to increase bandwidth.

Another thing to consider is the latency of requests. It takes a looong time to make a round trip to the satellite, so if you are making lots of small requests (like DNS and HTTP requests when loading a web page) the upload speed can seem slower than it actually is and increased bandwidth won’t help.

Increasing internet performance by ganging multiple connections can be problematic - each connection ends up with it’s own ip address, and all the elements of a connection need to originate from the same IP address to allow it to work. It can be done, but the gains do not generally scale linearly. Your costs will increase faster than your effective upload speed. You will need to spend some money on a very smart router to handle the aggregation, too.