What's the latest software I can upgrade on my iMac Pro OSX 10.6.7? (2011)

The info you stated was just enough to trace this model in MacTracker:

• iMac (27-inch, Late 2009)

Introduced October 2009

Discontinued July 2010

Model Identifier iMac10,1 (Core 2 Duo) iMac11,1 (Core i5, or i7)

Model Number A1312

EMC 2309 (Core 2 Duo) -or- EMC 2374 (Core i5, or i7)

Order Number MB952LL/A (3.06 GHz), MB953xx/A (2.66 GHz)

Software

Original OS Mac OS X 10.6.1 (10A2155), 10.6.2 (10C2234)

Maximum OS macOS 10.13.6 (17G65) High Sierra

Link(s) w/ information detail on how to begin download an installer:

• How to get old versions of macOS - Apple Support

https://support.apple.com/en-us/HT211683

macOS High Sierra 10.13 can upgrade Sierra, El Capitan, Yosemite, Mavericks, Mountain Lion, Lion

• How to reinstall macOS - Apple Support

https://support.apple.com/en-us/HT204904

Should you need to use other installer methods or erase/install anew

some of that (disk utility, etc) info is within 'how to reinstall' link above.

Depending adequate free (unused) hard drive capacity, and have

backups -including Time Machine on dedicated HDD- this may do.

Additional info: https://everymac.com/ultimate-mac-lookup/

Good luck & happy computing!

🌞🌿⛵️🌤🎣🤖🏕🐝⛄️🌻

PS: In order to gain access to the Mac app store

your iMac may need to see update to Snow Leo

to 10.6.8 and then 'latest last' update, too.

• Download Mac OS X 10.6.8 Update v. 1.1

https://support.apple.com/kb/DL1400?locale=en_US

Then your Mac could 'see' an App Store.

This may be needed too:

• Mac App Store Update for OS X Snow Leopard 10.6.8

https://support.apple.com/kb/DL1860?locale=en_US

The internal menu software update button may still work

to try & get those last steps; and a Combo update version

to 10.6.8 would be among those. There had been several.

• Not sure at this point; having reread your original post

& considered the issues without Snow Leopard 10.6.8..

Perhaps you can avoid need to actually buy(?) Lion 10.7.5.

(None of mine had to go this path.)

You may need to download El Capitan (bootable installer)

from instructions instead of that High Sierra; that'd be later.

Those details are lower in this page:

• How to get old versions of macOS - Apple Support

https://support.apple.com/en-us/HT211683

A good brand of matching RAM upgrade chips for to

help your Mac run better with newer system load, is

advised upgrade in hardware. And hope HDD is OK.

Take care & good luck!

🌞🌿🎣🌤🐢⛵️🐟🐌📬