Like Seva suggested you can split up your file in chunks. I used this to split up my 4MB file
public static void main(String[] args) throws Exception {  
    String base = "tracks";  
    String ext = ".dat";  
    int split = 1024 * 1024;  
    byte[] buf = new byte[1024];  
    int chunkNo = 1;  
    File inFile = new File(base + ext);  
    FileInputStream fis = new FileInputStream(inFile);  
    while (true) {  
      FileOutputStream fos = new FileOutputStream(new File(base + chunkNo + ext));  
      for (int i = 0; i < split / buf.length; i++) {  
        int read = fis.read(buf);  
        fos.write(buf, 0, read);  
        if (read < buf.length) {  
          fis.close();  
          fos.close();  
          return;  
        }  
      }  
      fos.close();  
      chunkNo++;  
    }  
  }  
If you do not need to combine the files into a single file on the device again, just use this InputStream, which combines them into one on the fly.
import java.io.IOException;  
import java.io.InputStream;  
import android.content.res.AssetManager;  
public class SplitFileInputStream extends InputStream {  
  private String baseName;  
  private String ext;  
  private AssetManager am;  
  private int numberOfChunks;  
  private int currentChunk = 1;  
  private InputStream currentIs = null;  
  public SplitFileInputStream(String baseName, String ext, int numberOfChunks, AssetManager am) throws IOException {  
    this.baseName = baseName;  
    this.am = am;  
    this.numberOfChunks = numberOfChunks;  
    this.ext = ext;  
    currentIs = am.open(baseName + currentChunk + ext, AssetManager.ACCESS_STREAMING);  
  }  
  @Override  
  public int read() throws IOException {  
    int read = currentIs.read();  
    if (read == -1 && currentChunk < numberOfChunks) {  
      currentIs.close();  
      currentIs = am.open(baseName + ++currentChunk + ext, AssetManager.ACCESS_STREAMING);  
      return read();  
    }  
    return read;  
  }  
  @Override  
  public int available() throws IOException {  
    return currentIs.available();  
  }  
  @Override  
  public void close() throws IOException {  
    currentIs.close();  
  }  
  @Override  
  public void mark(int readlimit) {  
    throw new UnsupportedOperationException();  
  }  
  @Override  
  public boolean markSupported() {  
    return false;  
  }  
  @Override  
  public int read(byte[] b, int offset, int length) throws IOException {  
    int read = currentIs.read(b, offset, length);  
    if (read < length && currentChunk < numberOfChunks) {  
      currentIs.close();  
      currentIs = am.open(baseName + ++currentChunk + ext, AssetManager.ACCESS_STREAMING);  
      read += read(b, offset + read, length - read);  
    }  
    return read;  
  }  
  @Override  
  public int read(byte[] b) throws IOException {  
    return read(b, 0, b.length);  
  }  
  @Override  
  public synchronized void reset() throws IOException {  
    if (currentChunk == 1) {  
      currentIs.reset();  
    } else {  
      currentIs.close();  
      currentIs = am.open(baseName + currentChunk + ext, AssetManager.ACCESS_STREAMING);  
      currentChunk = 1;  
    }  
  }  
  @Override  
  public long skip(long n) throws IOException {  
    long skipped = currentIs.skip(n);  
    if (skipped < n && currentChunk < numberOfChunks) {  
      currentIs.close();  
      currentIs = am.open(baseName + ++currentChunk + ext, AssetManager.ACCESS_STREAMING);  
      skipped += skip(n - skipped);  
    }  
    return skipped;  
  }  
}
Usage:
ObjectInputStream ois = new ObjectInputStream(new SplitFileInputStream("mytempfile", ".dat", 4, getAssets()));