A Claisen condensation between two different esters is called a crossed Claisen condensation. There are two main types of crossed Claisen that we will go over in this post. One is the reaction between esters, both having alpha hydrogens, and the other is when only one of the partners has alpha hydrogens.
If both esters have ɑ hydrogens, the reaction is not synthetically useful since four products are obtained and it is difficult to separate them:

Therefore, just like the aldol reactions, efficient crossed Claisen condensation is possible in two scenarios:
One of the esters does not have α (alpha) hydrogens and therefore, it cannot form an enolate.
Ethyl benzoate and ethyl formate are the two common esters lacking ɑ hydrogens that are used in the crossed Claisen condensation.

The issue of self-condensation is something to always consider. For example, even though ethyl benzoate has no alpha hydrogens, reducing the number of products, the possibility of self-condensation of ethyl acetate is not eliminated.
And to prevent this, the concentration of ethyl acetate should be kept very low. So, we mix the ethyl benzoate (red) with the base and add the ethyl acetate (blue) to this solution. This ensures that at any given time, there is a large excess of the ethyl benzoate and all the enolate of the ethyl acetate is consumed as it is created.
Ethyl formate is especially suitable for crossed Claisen reactions since, in addition to not having an ɑ hydrogen, it also resembles an aldehyde which are more reactive as electrophiles toward enolates:

Crossed Claisen with LDA
The second possibility for doing crossed Claisen is the use of LDA as a strong, sterically hindered base to irreversibly deprotonate one of the esters. This approach allows to selectively convert one of the esters into an enolate and keep the other one as is to serve as the electrophile:

Claisen Condensation with Ketones
A nice variation of the Claisen condensation is the reaction of esters with ketones. Three esters are especially useful for this: the ethyl formate that we saw above, ethyl chloroformate, and diethyl carbonate:

Again, what’s special about these esters is their higher reactivity. This allows overcoming the competing aldol condensation of the ketone which forms a β-hydroxy carbonyl. Now, the advantage of the Claisen reaction is that, despite being an unfavorable equilibrium, the β-keto ester final product is easily and irreversibly deprotonated thus shifting the equilibrium forward. See the diagram below showing the competition between Claisen and Aldol reactions:

Refer, to the Claisen condensation post for more details and check the following links to do some more practice on Claisen condensation and enolate chemistry in general:
Claisen Condensation Practice Problems
Enolates in Organic Synthesis – a Comprehensive Practice Problem
Check Also
- Alpha Halogenation of Enols and Enolates
- The Haloform and Iodoform Reactions
- Alpha Halogenation of Carboxylic Acids
- Alpha Halogenation of Enols and Enolates Practice Problems
- Aldol Reaction – Principles and Mechanism
- Aldol Condensation – Dehydration of Aldol Addition Product
- Intramolecular Aldol Reactions
- Aldol Addition and Condensation Reactions – Practice Problems
- Crossed Aldol And Directed Aldol Reactions
- Crossed Aldol Condensation Practice Problems
- Alkylation of Enolates Alpha Position
- Enolate Alkylation Practice Problems
- Acetoacetic Ester Synthesis
- Acetoacetic Ester Enolates Practice Problems
- Malonic Ester Synthesis
- Michael Reaction: The Conjugate Addition of Enolates
- Robinson Annulation, Shortcut, and Retrosynthesis
- Claisen Condensation
- Dieckmann condensation – An Intramolecular Claisen Reaction
- Crossed Claisen and Claisen Variation Reactions
- Claisen Condensation Practice Problems
- Stork Enamine Synthesis
- Enolates in Organic Synthesis – a Comprehensive Practice Problem