The support for creating embeddings for batch sizes > 1 would be dependent upon the methods and tools that the specific codebase provides. If the particular project this class is from supports a batch processing approach, it is likely that this would be possible. However, the limitation specified for this class suggests that the batch size is restricted to 1. Therefore, another handling approach or class would likely be needed to process larger batch sizes.

For the second question, the provision to support more ways of initiating embedding_builder would greatly depend on whether there were more subclasses of SymbolEmbeddingBuilder that could be used as alternatives to SymbolDocEmbeddingBuilder. For instance, if there were various kinds of embedding builders for different kinds of symbols, then it would be reasonable to expand the functionality of the handler to accommodate these different builders. However, it would likely require significant modification of the SymbolDocEmbeddingHandler class to allow for different kinds of embedding builder objects to be used. If the project’s architecture allows the creation or utilization of different symbol embedding builders, it could be a potential enhancement. Still, it’s important to note the specificity of the task at hand which is processing embeddings for Python symbols from source code - a task well suited for SymbolDocEmbeddingBuilder.