Sure you can

It's possible but I agree with Ms Help on the formal/informal stuff. Besides, if you use "e.g./for example/like/such as/for instance" it's basically understood that there are other options. "I like football teams with red shirts such as Manchester United, Liverpool, Bayern etc." "I like football teams with red shirts such as Manchester United, Liverpool and Bayern." Both sentences are okay. I think that in the first sentence the emphasis is more on the red shirt and the second sentence kinda suggests that those three teams are the ones you like most. Anyway, like Ms Help said, 'etc.' is a bit less formal.

I just googled for some resources in this field. And it seems that it is not suggested that we those words together, because the repetitive usages of words are not recommended in some formal writing styles. Check the following if you need more references. i.e.: Latin abbreviation for id est, which means“that is，in other words” e.g.: Latin abbreviation for exempli gratia, which means“for example" etc. stands for etcetera, means "and so on” Using e.g. and etc. in the same sentence is not suggested.