2. After the issue discussion, you can also mention the opportunity to share the suggestions with the user using:

"I've also taken a look at your site and must note that the bags you sell look really stylish and comfortable! + It would also be a great idea to add wishlist feature to your store, so ..."
3. Escalation / Chat Transfer: 

"And I’ll also take a look at the site to see if there are any suggestions I may offer to you once we discuss the issue/domain question. Is it okay with you? Great! Thanks"

2. (Do the same as for chats +)Once you checked a user's issue (and had a minute to take a look at the site and account), and get back to them with your findings, you can also make a compliment, ask a question about their site/business + use this info for presenting the suggestion once the issue is discussed (Step 2 for chats):
"Thank you for waiting, I'm back! Before we dive deeper into the issue discussion, I should say that I've taken a look at your site and noticed you own an animal shelter. Your mission is amazing, as it's so important to help animals"
+ mention you have a suggestion which you'd like to present after the issue solution

3. Escalation/transfer case: before ending up the call to esc it offline or transfer to another live queue, you can also mention the suggestion:
"Before transferring the case to our advanced team, I'd like to make our call beneficial for you and provide a small tip for your site development. It'll take just a couple of minutes. How does it sound?"

4. It sometimes happens that you're checking the issue with the advanced team and waiting for their reply. It's also possible to say about suggestion and present it during the downtime:
"I'm currently waiting for the update from the advanced team. Meanwhile, I'd like to tell you about the tool which you can benefit from. What do you think?"