I have imac from mid 2011 with OS High Sierra 10.13.2. Is there any way to upgrade my OS at all?

sure, I believe so, mkozmk. Your iMac will run El Capitan. It will not run Mojave or anything later than that. At least not officially. and I can't talk about the other way, so I won't. Here's a link to El Capitan for your convenience:

https://support.apple.com/en-us/HT206886

you'll need an Ethernet cable plugged into your iMac and enough RAM on board

that's it

john b

Check those facts. The OP hasn't asked about a downgrade. He/she needs the 10.13.6 Combo update:

https://support.apple.com/kb/DL1970?viewlocale=en_US&locale=en_US

It is 2.49 GB, not 8GB.

It can be updated to 10.13.6, but not past that.

(180968)

Johnb-one wrote:

sure, I believe so, mkozmk. Your iMac will run El Capitan.

FWIW, El Capitan would be a downgrade from High Sierra.

mkozmk wrote:

I have Wi-Fi wondering why I need to use ethernet cable?

FWIW, you don't need to. Sometimes an ethernet is more stable. A stable WiFi connection will work.

It’s just way faster& more reliable. If you do decide to upgrade, don’t let your mac go to sleep while doing so. The upgrade is about 8 gigs in size if that helps any

jb