Yes, depending on your definition of "combining features"
First, here's a good 'tree' of many languages in the Indo-European category.
See how many languages there are? And this doesn't even have many dialects on it (for example, it has Irish but not subdivided into Connacht, Munster, Ulster, etc.).
Now consider that this is just one possible organization. There are many languages that include words/grammar generally associated with one language family but not another.
Let's talk about Italo-Celtic. Italo-Celtic is a proposed grouping of the Italic (Latin and other Romance languages mostly) and the Celtic (Gaelic, Welsh, Breton, etc.) languages.
These are completely different groups, so why are they considered similar? They share some of the same characteristics, such as a long i (ī) in the genitive (2nd declension for Latin, female 2nd for Irish), similar superlative suffixes (ismo, em), and a merging of the aorist and perfect tenses. There's also some vocabulary, but similar words aren't quite as convincing as grammar and morphology.
This likely is the result of a Proto-Italo-Celtic language that both of the subgroups descended from.
But Italo-Celtic is more a supergroup than an in-between group. Are there any real "in-the-middle" branches?
The answer is no under the current classification scheme, mainly due to the fact that that makes no sense. The goal of a classification is for everything to fit neatly into a category, so the categories are pretty broad. You won't find anything that's quite in-between groups, though there are plenty of languages like Albanian that are grouped in their own category.
Generally, when linguists find related languages that aren't quite the same, they group them into another Indo- group. Indo-Iranian (containing Indo-Aryan and Iranian groupings) and Balto-Slavic (with Baltic and Slavic groupings) are good examples. Instead of having languages that are part of both groups, they subdivide the groupings closer and call them 'cousins'.
This goes to show that all of our beautiful classification scheme is only mortal and not infallible. With the way languages work, any geographically close languages may undergo some mixing. Linguistic categories today aren't necessarily the same in a couple centuries, or millennia.
So, mixed branches definitely exist, but it all depends on what time period you're in and what classification scheme you're using.