Is it correct to use two present participles sequentially?
We are currently in the process of finishing planning for the outage.
It the preceding sentence grammatically correct?
Is the preceding sentence ideally structured?
If not, what would be a better way of saying it?
Solution 1:
"We are currently in the process of finishing planning for the outage."
There can be grammatical constraints on some types of double "-ing" phrases.
I'll mention some of them here, and let you decide how applicable they are to your example.
Double -ing constraint:
CGEL page 1243-4:
The double-ing constraint
Some verbs that license gerund-participial complements cannot themselves occur in the gerund-participle form when they have such a complement. Compare:
[37]
i a. They started quarreling. - - - b. (*) They are starting quarreling.
ii a. The lawn needs mowing. - - - b. (*) The lawn is always needing mowing.
iii a. We considered buying one. - - - b. We are considering buying one.
The succession of gerund-participles in [i.b/ii.b] is excluded by what is known as the 'double-ing constraint'. As evident from [iii.b], it applies to only a subset of catenative verbs -- a small subset, in fact. The clearest cases are aspectual verbs such as begin, cease, continue, start, stop, and verbs taking concealed passives, like need i [ii]. We should probably also include others, such as intend, but there is a good deal of variation between speakers as to their acceptance of the [b] construction. We noted in &1.1. that gerund-participials cannot have the progressive auxiliary be as head ( (*)They accused him of being running away when the alarm sounded), and this can be seen as a special case of the constraint.
Note that "finish" is an aspectual verb. CGEL page 1228:
Most aspectual verbs have raised subjects, . . . there are, however, a few that have ordinary subjects, normally with an agentive interpretation: discontinue, finish, quit, resume . . .
CGEL page 1174 fn1:
Examples with progressive be are occasionally encountered in casual speech: I've missed endless busses through [not being standing at the bus stop when they arrived]. This cannot, however, be regarded as an established construction in Present-day English.
It seems that you have got yourself a good ear. :)
Note that CGEL is the 2002 reference grammar by Huddleston and Pullum et al., The Cambridge Grammar of the English Language (CGEL).
Solution 2:
This is an example of what Ross (1970) calls the "Doubl-ing Constraint".
Zwicky (1999) is a very clear introduction to the phenomenon, with excellent examples, including
- It continues to rain.
- It continues raining.
- It is continuing to rain.
which are all grammatical, compared to the ungrammatical
- *It is continuing raining.