I bought these items:
1. https://www.amazon.de/-/en/dp/B09NSDPMRJ (1 x Aluminium Heatsink 300 mm x 25 mm x 10 mm Heatsink Module Cooling Fin for LED Cooling LED Emitter Diodes High Performance Splitter, Heatsink)
2. https://www.amazon.de/dp/B07JQD232W (Akuoly Set of 4 Aluminium Heatsink PC Cooling Fins Cooler Set Heatsink with Thermal Adhesive Tape Cooler Fin for Amplifier Transistor Semiconductor 70 mm x 22 mm x 6 mm Silver).
3. https://www.amazon.de/dp/B00XQ9AZ8Y (EC360® Glue 2W/mK Thermal Adhesive Liquid (10g))
I cut the longer blade in 3 parts for my three CompacF's, used the above glue to extend the heat sink with another 10cm of aluminium heatsink. Then for extra heat dissipation I add the smaller sinks on the back using same adhesive glue
-SNIP-
That thermal glue you are using is really poor thermal conductivity. You'll basically loose most of the benefit of a larger heatsink due to the poor thermal conductivity of the glue.
If you're going to glue heatsinks together you'll need a better thermal conductivity glue, 2W/mK just isnt going to cut it.
Most basic silicon thermal paste is in the region of 6W/mK, there are some pastes that are in the 9-12W/mK but rarely any better than this.
There's a 7.2W/mK glue available through Farnell https://uk.farnell.com/omega/ob-101-2/adhesive-epoxy-twinpack-2oz/dp/3870429 if you insist on gluing heatsinks together.
Anyway, if you want to improve the thermal performance you'd probably do better by completely replacing the original heatsink with something larger more fins, bigger surface area and using a good thermal conductivity paste or thermal pad to the ASIC.
Also, use a black annodised heatsink. It will offer a 5-10% improvement due to black body radiation.