Can I use 又 to give more than two properties of something?
There is a set phrase in Cantonese which goes:
又平又靓又正
ABC Canto defines it as:

STATIVE VERB
(for goods or services) to be not only cheap and attractive, but also good-quality; to be not only cheap and nice-looking, but also reliable

and gives the examples:

其實呢度都幾好買,啲衫又平又靚又正
kei4 sat6 ni1 dou6 dou1 gei2 hou2 maai5, di1 saam1 jau6 peng4 jau6 leng3 jau6 zeng3
In fact buying here is quite good, the clothes are not only cheap and attractive, but also good-quality
大陸人好鍾意嚟香港買嘢,係因為啲嘢又平又靚又正㗎
daai6 luk6 jan4 hou2 zung1 ji3 lai4 hoeng1 gong2 maai5 je5, hai6 jan1 wai6 di1 je5 jau6 peng4 jau6 leng3 jau6 zeng3 gaa3
China-mainlanders like to come to Hong Kong to buy things, it's because the things are not only cheap and nice-looking, but also reliable

Which should go to show that more than two 又s is okay.
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The issue you have with your example sentence that people are trying to correct you on is that the descriptors surrounded by the 又s need to go together.
Fast and good looking is lacking any sort of logical connection.
You could say: fast and nimble or good looking and cute.
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Slightly unrelated but you might want to know:
There’s also the new expression:
又双叒叕
you4 shuang1 ruo4 zhuo2 -or- you4 you4 you4 you4 you4 you4 you4 you4 you4 you4
To express that somethings happened yet again.
Here’s a headline from the recent news:

Windows10免费升级又双叒叕延期了