Yes, but...
When we sell a logo, we transfer the copyright to the buyer. We no longer own that logo! So the design that we make for you can not be too similar to the original. We use the same criteria as used by the trademark office: If there's a chance that people will confuse two logos, then they are too similar. Ultimately we want both your logo and the original to be "trademarkable". They should be that different.
That said, we can develop a logo for you in the same style, or using the same basic concept.
To proceed, we need you to place an order for a custom logo. Our entry level package would be sufficient since you already know what you want in the logo. On the order form, mention the product number of the logo that you liked (the product number is displayed to the left of the logo) and tell the design team to create something similar for you.
Here's a page that shows our custom logo packages and prices:
https://www.biz-logo.com/side-by-side.shtml
Tip: If there are two or more logos that you like, why not have our design team combine them for you! Use the same process as described above.