There are two points in the English Vocabulary Profile that relate to ‘way‘ in regards to manner:
way MANNER
C1[no plural] the manner in which someone behaves or thinks, or in which something happens
For example:
How do we measure changes in behavior in a meaningful way that‘s going to help us with prevention of disease,
early onset of disease, and tracking the progression of disease over a long period of time?
in a big way INFORMAL
C2 used to say that someone or something does something to a large degree
For example:
The Japanese are here in a big way.
A search in NOW corpus for:
_VV in _A _J way
1 BEHAVE IN A CERTAIN WAY 522
2 WORKS IN A SIMILAR WAY 485
3 WORK IN A SIMILAR WAY 426
4 USED IN THE RIGHT WAY 276
5 SERVED IN THE ORDINARY WAY 274
6 ACT IN A CERTAIN WAY 253
7 CONTRIBUTE IN A MEANINGFUL WAY 158
8 OPERATE IN A SIMILAR WAY 156
9 THINK IN A DIFFERENT WAY 136
10 CHANGE IN A BIG WAY 124
11 CONTRIBUTE IN A BIG WAY 119
12 PLAY IN A DIFFERENT WAY 119
13 PLAY IN A CERTAIN WAY 115
14 USED IN A SIMILAR WAY 111
15 USED IN A POSITIVE WAY 106
16 OPERATES IN A SIMILAR WAY 102
17 GOING IN THE RIGHT WAY 102
18 HELP IN A BIG WAY 95
19 WORK IN A DIFFERENT WAY 95
20 VOTE IN A PARTICULAR WAY 94
21 CONTRIBUTE IN A POSITIVE WAY 94
22 CHANGED IN A BIG WAY 86
23 TREATED IN A SIMILAR WAY 85
24 CONTRIBUTED IN NO SMALL WAY 82
25 BLOG IN AN EASY WAY 82
26 BEHAVE IN A PARTICULAR WAY 82
27 RESPOND IN THE RIGHT WAY 81
28 WORK IN A BIPARTISAN WAY 79
29 HELP IN A SMALL WAY 79
30 PREPARE IN THE RIGHT WAY 75
31 RESPOND IN A POSITIVE WAY 74
32 BEHAVING IN A CERTAIN WAY 71
33 RESPONDED IN A BIG WAY 67
34 OPERATE IN A DIFFERENT WAY 67
35 ENGAGE IN A MEANINGFUL WAY 66
36 USED IN A DIFFERENT WAY 66
37 VOTE IN A CERTAIN WAY 66
38 TREATED IN A DIFFERENT WAY 65
39 GROW IN A SUSTAINABLE WAY 65
40 DRESS IN A CERTAIN WAY 65
41 CHANGED IN A MEANINGFUL WAY 65
42 BENEFIT IN A BIG WAY 64
43 DELIVERED IN A BIG WAY 64
44 HANDLED IN THE RIGHT WAY 62
45 CONTRIBUTING IN A BIG WAY 62
46 WORKS IN A DIFFERENT WAY 62
47 REBOUNDED IN A BIG WAY 61
48 REACT IN THE RIGHT WAY 59
49 ACT IN A PARTICULAR WAY 58
50 CELEBRATED IN A BIG WAY 57
51 CONTRIBUTE IN A SMALL WAY 56
52 ACT IN A SIMILAR WAY 54
53 FELT IN A BIG WAY 54
54 HAPPENING IN A BIG WAY 53
55 DIVIDED IN A DIFFERENT WAY 53
56 CONTRIBUTED IN A BIG WAY 51
57 REBOUND IN A BIG WAY 49
58 BEHAVE IN A DIFFERENT WAY 48
59 HELPED IN NO SMALL WAY 47
60 APPROACHED IN THE RIGHT WAY 47
61 PARTICIPATE IN A MEANINGFUL WAY 47
62 RESPOND IN THE BEST WAY 47
63 RESPOND IN A TIMELY WAY 46
64 USHER IN A NEW WAY 45
65 REACT IN A CERTAIN WAY 45
66 BEHAVE IN A SIMILAR WAY 42
B2: contribute, contributed, contributing, meaningful, participate, react, respond, responded, treated
C1: engage, sustainable