¹H NMR and MS analysis of products obtained by Claisen condensation reaction between methyl 2‐methylpropanoate and sodium methoxide
Looking at your comment, I believe the main source of confusion may be understanding the underlying reason why the Claisen condensation requires the two α protons.
The first one, obviously, is required for the enolate to form. The second one is arguably equally important because it is the removal of this proton in the condensed product that prevents a retro-Claisen. The Claisen condensation is equilibrium driven to the product by that last deprotonation. Under the conditions listed here, you cannot deprotonate the product to generate the &quot;real&quot; product, so a retro-Claisen will quickly take place to provide the original starting material.
The &quot;desired&quot; product is the bis-methylated β-keto ester. You cannot use the conditions for a Claisen, but, as mentioned in comments, alkylation of the unmethylated β-keto ester should work. If you use a strong electrophile, like methyl iodide, you shouldn't need any harsh basic conditions, especially given the fact that a β-keto ester is quite acidic.