Yes, it's possible to combine different analyzers in Lucene together.
You should use something like this:
StringReader reader = new StringReader(text);
Tokenizer whitespaceTokenizer = new WhitespaceTokenizer();
whitespaceTokenizer.setReader(reader);
TokenStream tokenStream = new StopFilter(whitespaceTokenizer, StopAnalyzer.ENGLISH_STOP_WORDS_SET);
tokenStream = new PorterStemFilter(tokenStream);
where text is a variable, containing something you want to be analyzed. Here I combine whitespace tokenization (probably you could replace it with StandardAnalyzer which is more sophisticated) and then I remove stop words with StopFilter and later in analyzer chain use a PorterStemFilter (which also more better than just simple EnglishStemmer, also you could replace it with any TokenFilter you like.
Complete example is available here - https://raw.githubusercontent.com/MysterionRise/information-retrieval-adventure/master/lucene4/src/main/java/org/mystic/StopWordsStemmingAnalyzer.java