Can I split an Apache Avro schema across multiple files?

Yes, it’s possible.

I’ve done that in my java project by defining common schema files in avro-maven-plugin
Example:

search_result.avro:

{
    "namespace": "com.myorg.other",
    "type": "record",
    "name": "SearchResult",
    "fields": [
        {"name": "type", "type": "SearchResultType"},
        {"name": "keyWord",  "type": "string"},
        {"name": "searchEngine", "type": "string"},
        {"name": "position", "type": "int"},
        {"name": "userAction", "type": "UserAction"}
    ]
}

search_suggest.avro:

{
    "namespace": "com.myorg.other",
    "type": "record",
    "name": "SearchSuggest",
    "fields": [
        {"name": "suggest", "type": "string"},
        {"name": "request",  "type": "string"},
        {"name": "searchEngine", "type": "string"},
        {"name": "position", "type": "int"},
        {"name": "userAction", "type": "UserAction"},
        {"name": "timestamp", "type": "long"}
    ]
}

user_action.avro:

{
    "namespace": "com.myorg.other",
    "type": "enum",
    "name": "UserAction",
    "symbols": ["S", "V", "C"]
}

search_result_type.avro

{
    "namespace": "com.myorg.other",
    "type": "enum",
    "name": "SearchResultType",
    "symbols": ["O", "S", "A"]
}

avro-maven-plugin configuration:

<plugin>
    <groupId>org.apache.avro</groupId>
    <artifactId>avro-maven-plugin</artifactId>
    <version>1.7.4</version>
    <executions>
        <execution>
            <phase>generate-sources</phase>
            <goals>
                <goal>schema</goal>
            </goals>
            <configuration>
                <sourceDirectory>${project.basedir}/src/main/resources/avro</sourceDirectory>
                <outputDirectory>${project.basedir}/src/main/java/</outputDirectory>
                <includes>
                    <include>**/*.avro</include>
                </includes>
                <imports>
                    <import>${project.basedir}/src/main/resources/avro/user_action.avro</import>
                    <import>${project.basedir}/src/main/resources/avro/search_result_type.avro</import>
                </imports>
            </configuration>
        </execution>
    </executions>
</plugin>