Yes you can, it all about planning your layout on the floor, if its a layout involving a lot of curves and circular patterns, bring your new router bits along for the ride.
Based on my 20 years of flooring work, It is generally conceivable to be able to cut an inlay into a existiting floor but not easy and is time consuming. To make this look good, here are some things to consider. If your talking about just a center pre-made pattern then it’s possible. If your talking about a walnut inlay along the perimeter of room than it’s not practical.
*you need to controll the straightness and sharpness of the cuts otherwise your final product may look less professional. If it’s oak you are asking about it hard to plunge a router and control finish edge and without burning. So you’ll need to have edge template to follow and take a multipul shallow cuts.
*if it’s an older floor, there is a possibility that the floor has been sanded multipul times and the thickness of the new floor will not match. So sanding & refinishing the entire area to make surfaces flat and level will be required.
My general experience with this work is that due to the way a wooden floor works, it floats and expands in multipul directions. Therefore when the inlay is installed on an existing floor, there is no real way to lock the tongue and groove on the starting edge. So perimeter of inlay tends to lift higher than the old floor. Over glueing it splits the wood over time. I have been sussecuful with a vibrating saw not a router. Built a template and took a lot of time. Generally speaking if it’s a big inlay or mutipul locations or perimeter inlay it just ain’t worth it.
Yes, custom inlays can be cut in virtually any floor. However, the cost will depend largely on how intricate the inlay is, as well as the existing condition of the floor. Custom inlays will usually require sanding and refinishing of the entire floor to obtain a quality result.