You need something like this: Makie.convert_arguments(p::Makie.PointBased, sol::ODESolution) = convert_arguments(p, sol.t, [[v[1] for v in sol.u], [[v[2] for v in sol.u]]])
Not sure if this will work, you have to supply a minimal working example.

We’re pretty close to pin down how Makie should do recipes in the future and then revamp the docs accordingly.

I’m also confused how recipes and argument conversion work and would be happy to see some more examples and detailed explanations in the Docs.
However, for plotting multidimensional solutions, I find it convenient to use series. Here is a MWE with what I use:

using DifferentialEquations
using GLMakie
function f!(du, u, p, t)
x, y = u
α, β, γ, δ = p
du .= [α*x - β*x*y, δ*x*y - γ*y]
nothing
end
prob = ODEProblem(f!, [0.1, 0.1], (0.0, 25.0), (α = 1, β = 1.5, γ = 1, δ = 2))
sol = solve(prob, saveat=0.1)
# plot solution using series
# 1: manually
GLMakie.series(sol.t, hcat(sol.u...); labels=["x", "y"])
axislegend()
# 2: convert arguments
Makie.convert_arguments(T::Type{<: Series}, sol::ODESolution) = Makie.convert_arguments(T, sol.t, hcat(sol.u...))
GLMakie.series(sol; labels=["x", "y"])
axislegend()