html = """
<html>
<head>header
</head>
<blockquote>blah blah
</blockquote>
<p>eiaoiefj</p>
<blockquote>capture this next
</blockquote>
<p></p><strong>don'tcapturethis</strong>
<blockquote>
capture this too but separately after "capture this next"
</blockquote>
</html>
"""
from bs4 import BeautifulSoup
soup = BeautifulSoup(html)
quote1 = soup.blockquote
quote1.text
quote2 = quote1.find_next_siblings('blockquote')
quote2.text
Поиск следующего встречающегося тега и заключенного в нем текста с помощью Beautiful Soup