Yeah, holes seem to happen in leptomyxa:
L[eptomyxa] reticulata is an edaphic protozoan and a predator of bacteria and amoebae. [...] The plasmodium is very polymorphic; its size varies between 50 .mu.m and 1 cm. It generally spreads in the form of a very thin transparent protoplasmic layer. It may have the shape of a full blade, sometimes perforated with holes, or of a network; the pseudopodial zones with active locomotion present a typical fan-shaped contour.
There are some hi-res images from other sources showing the same
Image source: http://penard.de/Amoebozoa/Tubulinea/Leptomyxida/
It seems that what happens is that branches "merge back" after touching "at the tips" leaving holes in such organisms, but that's just speculation on my behalf. I haven't (yet) found a source discussing the dynamics of how these holes get formed.
And a couple more images from a different source--a broader review of leptomyxidae.
[Above] Light microscopy of Leptomyxa arborea n. sp. and L. variabilis n. sp. (by S.
Geisen and C. Burberg) on the plastic bottom of a Petri dish (Phaco). A-F: Leptomyxa arborea,
various shapes and specimens of different size. G-M: Leptomyxa variabilis, various shapes of
trophozoites (G-K and M); cysts (L-M). Arrows indicate the most pronounced bunches of
adhesive filaments; arrowheads indicate pore like structures in cysts. Scale bar is 100 μm in A-E
50 μm in F-K and 25 μm in L-M.
[Above] Isolate of Leptomyxa sp. (by morphology of trophozoite indistinguishable from
L. reticulata) observed in the sample from Valamo Island, North-West Russia (by A.Smirnov).
A: usual appearance of a trophozoite. B-D: subsequent stages of contraction of the cell on the
object slide under the bright light beam. Figure D shows pseudopodia very similar to those or
Rhizamoeba; polypodial cell like this one can move relatively rapidly for some distance.
Molecualar data from this strain were not obtained. Scale bar is 50 μm.
By the way, the "branches" are more or less "legs"/"limbs" used in locomotion; but also this species is multinucleate:
Leptomyxa reticulata is the type species of the genus Leptomyxa. It is a
multinucleate, expanded organism with plasmodia-like organization of its ramose body,
possessing a simple life cycle [...] Moving amoebae usually form adhesive uroidal filaments along the posterior end of the body or an uroidal structure consisting of a pack(s) of such filaments (the latter often is seen when the locomotive cell adopts a shape of
an irregular ramose triangle, with the base directed anteriorly).
A more diagrammatic explanation:
Main morphological traits of leptomyxid amoebae. A-E: Leptomyxa cf. reticulata
(Valamo Island strain by AS). A: expanded, plasmodium-like ramose cell, slowly moving on the
substrate. This is the “textbook” appearance of Leptomyxa. B – more compact, faster moving and
actively feeding cell. C: Disturbed cell showing compact lobose pseudopodia. Leptomyxa accepts
shapes like this under certain influence (light, temperature, etc. in order to relocate rapidly). D:
solitary cyst with double wall. E: several cysts covered with the shared outer cyst wall (D-E are
drawn based on photos by Pussard and Pons 1976a)
(So yes, creepin' amoeba with holes and "limbs"!)
A more interesting question at this point is whether there are any (naturally occurring) single-nucleus examples of "cells with holes".