Are there any other types of counterpoint?
Yes! Outside of the Palestrina-style counterpoint described by Fux's "species" -- which is to say, Modal, and eventually Tonal, counterpoint -- there are a variety of approaches. Here are a few.
These two videos give brief introductions to serialism and to serial counterpoint, repsectively.
Melharmony is a system of developing polyphonic or contrapuntal music based in music systems that are fundamentally melodic; for example, Indian Classical music.
In this answer to the question Can modal counterpoint be studied without studying harmony? Where to start? there are a number of resources listed.
Many composers have explored counterpoint in microtonal compositions, though to date, I'm unaware of a unified approach. The book Steps to the Sea: Ear Training and Composing in a Minute Equal Temperament by Julia Werntz (2014, Frog Peak Music) lays out microtonal composition exercises in a form analogous to "species" exercises.
(See also: What is rhythmic counterpoint?)
Phasing is a technique primarily associated with composer Steve Reich. The basic concept is to create a musical line as a series of pulses, initial played in unison, but then slowly going out of phase with each other through progressive delays of each part.
A straightforward example is his Clapping Music (1972).
His piece Electric Counterpoint is a more elaborate example.
Termed by Olivier Messaiaen, a rhythmic canon is one such that "each instrument should play the same rhythm but start at a different time."1 Further, "if the rhythmic canon is such that at every time interval exactly one instrument can be heard, then the canon is said to be tiled."2
An example of a rhythmic cannon can be heard in Messaiaen's Harawi (1945) midway though "Part VII: Adieu".
Tom Johnson works especially with tiling rhythmic canons. For example, his piece Tilework for Trombone.
Much of the writing on (tiling) rhythmic canons is highly mathematical. The seminal paper by Daniel Vuza, “Supplementary sets and regular complementary unending canons”, can be found in Perspectives of New Music.3 Moreno Andreatta has written extensively on the subject. For more musically oriented papers, Tom Johnson has published several articles. Google Scholar is a good source for papers by both Andreatta and Johnson, as well as others.
1 http://archive.bridgesmathart.org/2009/bridges2009-265.pdf, accessed 2020 Sept 19.
3 D.T. Vuza, “Supplementary sets and regular complementary unending canons”, Perspectives of New Music, Nos. 29(2) pp. 22-49; 30(1) pp.184-207; 30(2) pp.102-125; 31(1), pp. 270-305, (1991).